Apparatus and method for evaluating a semiconductor wafer

ABSTRACT

An apparatus and method uses diffusive modulation (without generating a wave of carriers) for measuring a material property (such as any one or more of: mobility, doping, and lifetime) that is used in evaluating a semiconductor wafer. The measurements are carried out in a small area, for use on wafers having patterns for integrated circuit dice. The measurements are based on measurement of reflectance, for example as a function of carrier concentration. In one implementation, the semiconductor wafer is illuminated with two beams, one with photon energy above the bandgap energy of the semiconductor, and another with photon energy near or below the bandgap. The diameters of the two beams relative to one another are varied to extract additional information about the semiconductor material, for use in measuring, e.g. lifetime.

CROSS-REFERENCES TO RELATED APPLICATIONS

This application is a continuation application of Ser. No. 09/095,804 filed Jun. 10, 1998, by Peter G. Borden et al. and now U.S. Pat. No. 6,049,220 entitled “Apparatus and Method for Evaluating a Wafer of Semiconductor Material.”

This application is related to and incorporates by reference herein in their entirety, the following three commonly owned, copending U.S. patent applications:

Ser. No. 08/638,944, entitled “SYSTEM AND METHOD FOR MEASURING THE DOPING CONCENTRATION AND DOPING PROFILE OF A REGION IN A SEMICONDUCTOR SUBSTRATE”, filed Apr. 24, 1996, now U.S. Pat. No. 5,883,518, by Peter G. Borden;

Ser. No. 08/637,244, entitled “SYSTEM AND METHOD FOR MEASURING PROPERTIES OF A SEMICONDUCTOR SUBSTRATE IN A FABRICATION LINE,” filed Apr. 24, 1996, now U.S. Pat. No. 5,966,019, by Peter G. Borden; and

Ser. No. 09/095,805, entitled “AN APPARATUS AND METHOD FOR MEASURING A PROPERTY OF A LAYER IN A MULTILAYERED STRUCTURE,” filed Jun. 10, 1998, now U.S. Pat. No. 6,054,868, by Peter G. Borden et al.

BACKGROUND OF THE INVENTION

1. Field of the Invention

This invention relates generally to the evaluation of a wafer of semiconductor material, and in particular to the measurement of a property of the semiconductor material.

2. Description of Related Art

In the processing of a semiconductor wafer to form integrated circuits, charged atoms or molecules are directly introduced into the wafer in a process called ion implantation. Ion implantation normally causes damage to the lattice structure of the wafer, and to remove the damage, the wafer is normally annealed at an elevated temperature, typically 600° C. to 1100° C. Prior to annealing, material properties at the surface of the wafer may be measured, specifically by using the damage caused by ion implantation.

For example, U.S. Pat. No. 4,579,463 granted to Rosencwaig et al. (that is incorporated herein by reference in its entirety) describes a method for measuring a change in reflectance caused by a periodic change in temperature of a wafer's surface (see column 1, lines 7-16). Specifically, the method uses “thermal waves [that] are created by generating a periodic localized heating at a spot on the surface of a sample” (column 3, lines 54-56) with “a radiation probe beam . . . directed on a portion of the periodically heated area on the sample surface,” and the method “measure[es] the intensity variations of the reflected radiation probe beam resulting from the periodic heating” (column 3, lines 52-66).

As another example, U.S. Pat. No. 4,854,710 to Opsal et al. (also incorporated herein by reference in its entirety) describes a method wherein the density variations of a diffusing electron-hole plasma are monitored to yield information about features in a semiconductor” (column 1, lines 61-63). Specifically, Opsal et al. state that “changes in the index of refraction, due to the variations in plasma density, can be detected by reflecting a probe beam off the surface of the sample within the area which has been excited” (column 2, lines 23-31) as described in “Picosecond Ellipsometry of Transient Electron-Hole Plasmas in Germanium,” by D. H. Auston et al., Physical Review Letters, Vol. 32, No. 20, May 20, 1974.

Opsal et al. further state (in column 5, lines 25-31 of U.S. Pat. No. 4,854,710): “The radiation probe will undergo changes in both intensity and phase. In the preferred embodiment, the changes in intensity, caused by changes in reflectivity of the sample, are monitored using a photodetector. It is possible to detect changes in phase through interferometric techniques or by monitoring the periodic angular deflections of the probe beam.”

A brochure entitled “TP-500: The next generation ion implant monitor” dated April, 1996 published by Therma-Wave, Inc., 1250 Reliance Way, Fremont, Calif. 94539, describes a measurement device TP-500 that requires “no post-implant processing” (column 1, lines 6-7, page 2) and that “measures lattice damage” (column 2, line 32, page 2). The TP-500 includes “[t] wo low-power lasers [that] provide a modulated reflectance signal that measures the subsurface damage to the silicon lattice created by implantation. As the dose increases, so does the damage and the strength of the TW signal. This non-contact technique has no harmful effect on production wafers” (columns 1 and 2 on page 2). According to the brochure, TP-500 can also be used after annealing, specifically to “optimize . . . system for annealing uniformity and assure good repeatability” (see bottom of column 2, on page 4).

SUMMARY

A method in accordance with this invention: (1) creates charge carriers in a concentration that changes in a cyclical manner (also called “modulation”) only with respect to time, in a region (also called “illuminated region”) of a semiconductor material, and preferably also (2) maintains the charge carriers at an average concentration that remains the same (or at least approximately the same e.g. varies less than 10%) before and during a measurement indicative of the number of charge carriers created in the illuminated region by act (1).

In one embodiment (also called “scanning embodiment”), one or more such measurements are compared each with the other, thereby to identify a sudden change in the measurements. In another embodiment (also called “measurement embodiment”), one or more measurements are compared with similar measurements on wafers (also called “reference wafers”) processed under known conditions and having known properties, thereby to determine one or more process conditions or properties of a wafer under fabrication.

In one implementation, an attribute derived from measurements on a wafer is interpolated with respect to corresponding attributes of wafers having a known material property (or process condition), thereby to determine a corresponding property (or condition) of the wafer under measurement. An example of a process condition is the temperature (also called “annealing temperature”) at which the wafer is annealed. Examples of material properties include surface concentration, mobility, junction depth, lifetime and defects that cause leakage current at the junction (when the junction is reversed biased).

The charge carriers (also called “excess carriers”) being created and measured as described above are in excess of a number of charge carriers (also called “background charge carriers”) that are normally present in the semiconductor material (e.g. due to dopant atoms) even in the absence of illumination. Therefore, in the first act described above, a number of excess carriers are created in the above-discussed region (also called “illuminated region”), e.g. by focusing thereon a laser beam or an electron beam. The concentration of excess carriers is modulated, both at the surface and in the bulk only as a function of time (e.g. by modulating the intensity of the just-described laser or electron beam that is also called “generation beam”).

The frequency of modulation of the concentration of excess carriers is deliberately selected to be sufficiently low to avoid modulation in space (i.e. avoid the creation of a wave of charge carriers). A carrier concentration that is devoid of a wave in space is created when at least a majority of the charge carriers (i.e. greater than 50%) move out of the illuminated region by diffusion. Such a temporal modulation under diffusive conditions (also called “diffusive modulation”) is used to measure the reflectance caused by excess carriers, e.g. by detection of the intensity of a beam (also called a “probe beam”) reflected by the illuminated region at the modulation frequency.

In the second act, an average concentration (e.g. root mean square average) of the excess carriers is determined from a measurement of the above-described reflectance over the time period of a modulation cycle. The average concentration is maintained the same (or approximately the same) prior to and during the measurement of reflectance. Specifically, the creation of new charge carriers (also called “measurement-related” carriers) in addition to the background charge carriers and the excess carriers is minimized or avoided during the reflectance measurement, thereby to maintain the total carrier concentration at or about the just-described average prior to the measurements.

An apparatus (also called “profiler”) that implements the above-described method includes, in one embodiment, a source that produces a probe beam formed of photons of energy lower than the bandgap energy (the energy necessary to generate conduction electrons) of the semiconductor material. Use of such a probe beam source eliminates the measurement-related carriers and the resulting errors that are otherwise created by a prior art apparatus, e.g. in measuring the reflectance with a probe beam that has photons of energy greater than the bandgap energy of silicon (such as the He—Ne laser probe beam described at column 15, line 56 of U.S. Pat. No. 4,854,710).

In addition to the above-described probe beam source, the profiler also includes a photosensitive element (such as a “photodiode”) that is located in the path of a portion of the probe beam reflected by the illuminated region. The photosensitive element generates an electrical signal (e.g. a voltage level) that indicates the intensity of the probe beam portion reflected by the illuminated region. The intensity in turn indicates reflectance caused by the excess charge carriers (e.g. created by incidence of a generation beam).

So, in one embodiment, the intensity measurement is used by the profiler as a measure of the concentration of excess charge carriers in the illuminated region. In this embodiment, the profiler also includes a computer that is coupled to the photosensitive element to receive the electrical signal, and that is programmed to determine the value of a material property in the illuminated region from one or more such measurements.

In another embodiment, the profiler creates measurement-related carriers by use of a probe beam having photons at or slightly above the bandgap energy of the semiconductor material. Even in the presence of such measurement-related carriers, the profiler maintains the overall accuracy of a measurement of a material property (as described herein) within a predetermined limit (e.g. 10% error) by limiting the number of such measurement-related carriers to a small percentage (e.g. up to 10%) of the excess carriers.

In the just-described embodiment, a diffusive modulation of charge carriers is created by use of a generation beam that has a wavelength and power chosen so that the rate of carriers generated by this beam is sufficiently larger, e.g. one order (preferably two orders) of magnitude larger than the rate of carriers generated by the probe beam so as to make the latter negligible.

In one implementation, in addition to the above-described probe beam source, the profiler includes a source that produces a generation beam (formed of photons) having an intensity that is modulated at a sufficiently low frequency to avoid creation of a wave of charge carriers. The powers of the two beams are maintained by the profiler to be at least approximately the same. Other implementations have two beams that each have a power different from the other, and yet maintain the measurement-related carriers (created by the probe beam) at a negligible percentage (e.g. the probe beam has photons of energy higher than the bandgap energy but has a power that is half or one-fourth the power of the generation beam, assuming that the power of the reflected portion of the probe beam is detected with sufficient accuracy as described above).

Measurement of intensity of a reflected portion of the probe beam while (1) using diffusive modulation and (2) generating negligible (preferably none) percentage of measurement-related carriers is a critical aspect of one embodiment of the invention. One or more such measurements provide a measure of a process condition or a property of the semiconductor material in the illuminated region. Such measurements are performed in one embodiment after annealing to activate the dopants, thereby to obtain a measure that is more indicative of the electrical behavior of the devices being fabricated than a property that is measured prior to annealing (as described in U.S. Pat. No. 4,854,710).

The above-described intensity measurements (from which reflectance measurements are derived), and one or more properties (also called “material properties”) are preferably (but not necessarily) monitored during fabrication, to control a process step (e.g. to control annealing temperature of a wafer that has been ion implanted) used in fabricating a wafer. As the material properties are measured directly on the wafer undergoing fabrication (also called “patterned wafer” or “annealed wafer” depending on the stage of fabrication), a measurement as described herein increases yield, as compared to an off-line measurement of a test wafer's properties.

During operation, the profiler (described above) performs a number of reflectance measurements, each measurement being for a different value of a parameter used either (1) in the generation of the excess carriers or (2) in the measurement of the concentration of excess carriers. In one embodiment, the profiler fits two or more such measurements to one or more straight lines or to a curved line, and compares an attribute of the fitted line (e.g. compares a first order coefficient, also called “slope,” of the fitted line), with corresponding attributes of corresponding lines generated from such measurements on wafers having known properties, thereby to determine a material property corresponding to the fitted line.

Moreover, a process condition (e.g. the temperature at which a patterned wafer has been annealed) can also be determined from such comparison of reflectance measurements, if the process condition affects the semiconductor material. Depending on the implementation, the comparison can be performed either manually or by a computer.

In a first implementation, the parameter varied between the measurements is the average concentration of charge carriers that is controlled by, e.g., changing the power or the diameter of the generation beam used to generate the charge carriers. Thereafter, a material property, such as mobility (or junction depth) is determined from intensity measurements by comparison of the above-described attribute with the corresponding attributes of wafers having known mobilities (or junction depths).

In one example, the wafer is undoped and mobility is determined by computing the slope of a plot of the intensity measurement against the power of the generation beam. In another example, the wafer has doped regions, and mobility is determined by comparing a slope obtained from the measurements (in the same manner as the just-described slope for the undoped wafer) with slopes of wafers having known mobilities.

In a second implementation, the varied parameter is the distance between the two beams that are used in performing an intensity measurement. In two variants of this implementation, the location of either (1) the generation beam, or (2) the probe beam, is changed relative to the wafer. The material property determined from such intensity measurements is lifetime.

In a third implementation, the parameter that is varied is the relative size of the two beams used in the intensity measurement e.g. the diameter of the probe beam is changed (while keeping the power of the probe beam the same). In this implementation as well, the material property determined from the intensity measurements is lifetime.

In another embodiment (also called “polarized embodiment”), a laser beam that is linearly polarized is used as a probe beam (also called “polarized probe beam”). The polarized probe beam need not have photons of energy below the bandgap energy of the semiconductor material, i.e. a beam of photons at or slightly above the bandgap energy (as described above) can be used if polarized.

On reflection from the illuminated region, a plane of polarization of the probe beam rotates through two different angles, depending on the following two reflection coefficients: one coefficient in a plane (also called “surface plane”) of the surface of the illuminated region, and another coefficient in a plane (also called “normal plane”) perpendicular to the surface plane.

After reflection, a portion of the probe beam that has been reflected is interfered with another portion that was not reflected. Next, two measurements are made, specifically of the sum and difference signals generated by the interference. Thereafter, a difference (hereinafter “in-phase difference”) between the two measurements that is in phase with the modulation of charge carriers is determined using a phase detector. The in-phase difference signal provides a measure of the concentration of excess carriers in the illuminated region.

Thereafter, one or more of the material properties discussed above are determined by use of in-phase difference signal (instead of using the intensity measurement described above). Use of a polarized probe beam (as described herein) provides an increase in sensitivity of the measurement of material properties by about two orders of magnitude over the use of a non-polarized beam, because of the increased sensitivity of a phase detector used in the polarized embodiment (as compared to an amplitude detector that is otherwise used) to measure the power of the reflected portion of the probe beam.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1A illustrates, in a high level block diagram, a system including an apparatus (called “active dopant profiler”) in accordance with the invention.

FIG. 1B illustrates, in a graph, the temporal modulation of charge carriers by the active dopant profiler of FIG. 1A, without creation of a wave, in a critical aspect of one embodiment.

FIG. 1C illustrates, in a cross-sectional view, use of a probe beam and a generation beam, each beam focused coincident with the other by the active dopant profiler of FIG.

FIGS. 1D and 1E illustrate, in graphs, variation of a measurement of intensity of a portion of the probe beam reflected by the wafer of FIG. 1C, as a function of a piezoelectric voltage that controls the distance between the two beams of FIG. 1C along axis x (FIG. 1D) and axis y (FIG. 1E), the two axes being illustrated in FIG. 8A.

FIGS. 1F and 1G illustrate, in a cross-sectional view and a plan view respectively, beams 151 and 152 of FIG. 1C offset from each other, (and also superimposed in the view of FIG. 1F is a graph of the concentration 164 of excess charge carriers as a function of the distance from axis 161 of generation beam 151).

FIG. 1H illustrates, in a cross-sectional view, beams 151 and 152 of FIG. 1C wherein the diameter of probe beam 152 has been increased (e.g. by an order of magnitude) as compared to the diameter illustrated in FIG. 1C.

FIG. 11 illustrates, in a cross-sectional view, use of a common lens 815 to form probe beam 152 that has a smaller diameter at wafer surface 153 than generation beam 151, wherein the relation is reverse prior to passage through lens 815.

FIG. 2A illustrates, in a flowchart, the acts performed by the system of FIG. 1A in one implementation.

FIG. 2B illustrates, in a flowchart, creation of charge carriers by the generation beam of FIG. 1C.

FIG. 2C illustrates, in a flow chart, the acts performed by profiler 103 of FIG. 1A to align two beams for use in reflectance measurement with coincident beams.

FIG. 3A illustrates, in a graph, intensity measurements (made by the profiler of FIG. 1A in a scanning embodiment) plotted along y axis as a function of position along the x axis for three wafers.

FIG. 3B illustrates in a two-dimensional map, intensity measurements obtained from scanning an area 95×95 μm² of an annealed, ion implanted wafer.

FIG. 3C illustrates, in a key, values of intensity measurements (in units of microvolts) shown in the map of FIG. 3B.

FIG. 4A illustrates, in a flow chart, acts performed on intensity measurements (by the profiler of FIG. 1A) to determine a material property or a process condition during fabrication of the wafer.

FIG. 4B illustrates, in a graph, intensity measurements as a function of a parameter (e.g. generation beam's power) that is varied to obtain the measurement, and fitting of the intensity measurements to two straight lines 471L and 471H to obtain coefficients (e.g. slope and intercept) used in measuring semiconductor material properties and process conditions.

FIG. 5A illustrates, in a graph, intensity measurements plotted on the y axis as a function of the power of generation beam 151 (FIG. 1C) at the source plotted along the x axis for wafers annealed at four different temperatures.

FIGS. 5B and 5C illustrate, in graphs, the variation of fitcoefficients (specifically the high power intercept and the low power slope obtained from FIG. 5A) as a function of the temperature at which the wafer was annealed plotted along the x axis.

FIGS. 5D and 5E illustrate, in graphs, the just-described coefficients plotted along the y axis as a function of junction depth and surface concentration respectively.

FIG. 5F illustrates, in a graph, another attribute (specifically the inflection point) of a line in FIG. 5A plotted along the y axis as a function of the doping concentration on the x axis for wafers having four different junctions depths.

FIG. 5F1 illustrates, in a key, values of junction depth shown in FIG. 5F.

FIG. 5G illustrates, in a graph, a normalized attribute (specifically the normalized high power slope) plotted along the y axis as a function of the sheet resistance (in ohms per square) plotted along the x axis.

FIG. 5H illustrates, in a graph, the variation of high power slope m_(H) plotted along the y axis as a function of mobility plotted along the x axis.

FIG. 6A illustrates, in a graph, the spreading resistance profile SRP (plotted along the y axis) as a function of the depth d (plotted along the x axis) from wafer surface 153 (FIG. 1C).

FIGS. 6B and 6C illustrate relationships known in the prior art for the bulk mobility and the bulk lifetime for use in one embodiment of profiler 103.

FIG. 7A illustrates in a graph, a normalized intensity measurement plotted along the y axis as a function of the radius of the probe beam (in μm) plotted along the x axis for material with normal lifetime, and degraded lifetime.

FIG. 7B illustrates, in a graph, the concentration per unit volume (at wafer surface 153 in FIG. 1C, and called “surface concentration”) of the excess carriers plotted along the y axis as a function of the distance from axis 155 (FIG. 1C) of generation beam 151 plotted along the x axis for two materials: one with normal lifetime and the other with degraded lifetime (degraded by a factor of 10,000).

FIGS. 8A and 8B illustrate, in block diagrams, various components used in one implementation of the active dopant profiler of FIG. 1A.

FIG. 9A illustrates, in a graph, a variation of the logarithm of the surface concentration plotted along the y axis as function of the radial distance (from the central axis 155 of generation beam 151 shown in FIG. 1C) plotted along the x axis, obtained by numerical modeling.

FIG. 9B illustrates, in a cross-sectional diagram, a beam incident on a semiconductor material having a layer of dopants in a concentration greater than the concentration of dopants in the bulk material, and superimposed thereon a graph of the potential distribution resulting from illumination by the beam.

FIG. 9C illustrates, in graphs, carrier concentration n_(e) plotted along y axis as a function (obtained by numerical modeling) of the power P of the generation beam plotted along x axis for different doping concentrations.

FIG. 10A illustrates, in a schematic diagram, the rotation of a plane of polarization of a probe beam after reflection by the semiconductor material.

FIG. 10B illustrates, in a graph, the reflectance measurement plotted along the y axis as a function of angle of incidence of the probe beam plotted along the x axis, wherein solid and dotted lines show relative effect of a small increase in the index of refraction (dotted line higher index than solid) due to an increase in the surface carrier concentration of the two polarization components rs and rp.

FIG. 10C illustrates, in a vector diagram, an angle through which the polarization plane is rotated after reflection as illustrated in FIG. 10A.

FIG. 11 illustrates, in a flowchart, various acts performed by the active dopant profiler of FIG. 1A using a polarized probe beam as illustrated in FIG. 10A.

FIG. 12 illustrates, in a block diagram, another implementation of the active dopant profiler of FIG. 1A.

FIG. 13 illustrates, in a graph, the signal-to-noise ratio plotted along the y axis as a function of the concentration of carriers plotted along the x axis as straight lines for four different wavelengths of the probe beam.

DETAILED DESCRIPTION

A wafer fabrication system 100 (FIG. 1A) in accordance with the invention is used to create integrated circuit (abbreviated as “IC”) dice by processing a wafer to form a “patterned wafer”, measuring a material property of the patterned wafer, and adjusting the processing in real time if necessary. The just-described processing can include annealing, and the measurement of a material property can be performed on a patterned wafer after annealing, thereby to determine process conditions not obtainable by prior art methods, e.g. to determine anneal temperature from measurements on the annealed wafer. Measurements on patterned wafers during fabrication as described herein eliminates test wafers that may be otherwise required in the prior art solely to monitor the fabrication process, thus reducing costs. Moreover, measurements on annealed wafers as described herein provide a measure of one or more properties that are related to the electrical characteristics (such as processing speed) of the devices being fabricated, because annealing results in activation of the dopants used in the devices.

System 100 includes a wafer processing unit 101 that performs an act 211 (FIG. 2A) e.g. by operating an ion implanter 101I to create, in a wafer 104 (FIG. 1A), one or more regions (e.g. doped region 130 in FIG. 1C) that have dopant atoms (e.g. boron atoms in silicon). Instead of ion implantation, any other process for creating doped regions, e.g. chemical vapor deposition, epitaxial deposition, evaporation, diffusion, or plasma deposition can be used in unit 101 (FIG. 1A) to perform act 211.

Thereafter, a patterned wafer 105 having one or more patterns of doped regions is transferred to a rapid thermal annealer 102 (FIG. 1A) that may be included in system 100. Rapid thermal annealer (also called “annealer”) 102 performs an annealing act 213 (FIG. 2A), e.g. by heating wafer 105 (FIG. 1A) to a predetermined temperature (also called “annealing temperature”), e.g. to remove damage that is normally caused by ion implanter 101 to the lattice structure of the semiconductor material in the doped regions of wafer 105. Instead of a rapid thermal annealer, a furnace may be included in system 100 and used to anneal wafer 105 in act 213 (FIG. 2A).

Annealing in act 213 causes the dopant atoms (also called “dopants”) to move into the lattice of the semiconductor material in a doped region 130, where the dopants act as donors (forming n-type material) or acceptors (forming p-type material). The extent to which the dopants incorporate into the lattice structure during act 213 is a function of the temperature at which and the time for which act 213 is performed. The incorporation is more complete at a higher temperature or after a longer time.

However, the dopants also diffuse (i.e. move) during act 213, thereby increasing the junction depth. The diffusion proceeds more rapidly at a higher temperature, and it is necessary to carefully control the annealing temperature. Therefore, a profile of the concentration of dopants as a function of depth is measured after act 213, and the profile is compared with predetermined information (e.g. a specification or profiles of wafers known to be good) to determine a change (if any) to be made to the annealing process. Dynamic feedback of such to-be-made changes to the annealing process in real time as described herein improves the yield of good wafers obtained from annealing in a manner not otherwise possible in the prior art.

Therefore, an annealed wafer 106 (FIG. 1A) is transferred from rapid thermal annealer 102 to a measurement device (hereinafter “active dopant profiler” or “profiler”) 103, and positioned therein (see act 220 in FIG. 2A). In an alternative embodiment, an active dopant profiler is integrated into a rapid thermal annealer and does not require positioning after completion of anneal. In one embodiment, profiler 103 is moved relative to wafer 106 instead of moving wafer 104.

Also, a non-annealed wafer 105 can be used (moved via path 109 in FIG. 1A) as illustrated by branch 212 in FIG. 2A e.g. if dopant regions do not require annealing due to use of a method other than ion implantation, such as diffusion (wherein dopants are diffused into wafer 105 thermally, and are active, and there is no need to anneal out implant damage). Profiler 103 evaluates the efficacy of the-dopants in a nonannealed wafer 105 in a manner similar to that described above for annealed wafer 106. A starting wafer 104 can also be used as illustrated by path 112 in FIG. 1A and by branch 215 in FIG. 2A. Therefore, in the following description, the notation “104/105/106” is used to indicate that the description is equally applicable to each of wafers 104, 105 and 106. Similarly the notation “105/106” indicates each of wafers 105 and 106.

Next, after a wafer 104/105/106 is properly positioned, profiler 103 creates (see act 230 in FIG. 2A) in a region of the wafer, a number of charge carriers that are modulated at a predetermined frequency. The predetermined frequency is selected to ensure that a wave of the charge carriers is not created during the act of measurement (see act 240 in FIG. 2A). As profiler 103 does not use a “plasma wave” as described in U.S. Pat. No. 4,854,710, profiler 103 is as effective in measuring a property of an annealed wafer 106 as in measuring a property of a non-annealed wafer 104/105.

Profiler 103 (FIG. 1A) measures a property (in act 240 in FIG. 2A) that is affected by charge carriers present in a doped region 130 (FIG. 1C) in a wafer 105/106, In one implementation, profiler 103 measures the reflectance that is thereafter used to determine various properties such as mobility, junction depth, surface carrier concentration, doping concentration, lifetime, and the number of active dopants as a function of depth “d” from surface 153 of wafer 105/106. A function (called “active dopant profile”) can be plotted in a graph as illustrated in FIG. 6A described below. In act 240, instead of the reflectance, profiler 103 can measure other properties affected by the created charge carriers, such as the refractive index.

One or more of these measurements are used (see act 260 in FIG. 2A) to determine if annealed wafer 106 conforms to the specification for such wafers. If wafer 106 conforms to the specifications, wafer 106 is identified as acceptable (e.g. by movement in the direction for further processing) and the conditions in wafer processing unit 101 (FIG. 1A) and in rapid thermal annealer 102 are left undisturbed. Thereafter, the above-described acts are repeated (as illustrated by branch 275) on another wafer or after further processing on the same wafer.

If a wafer 106 does not conform to the specifications, wafer 106 is identified as unacceptable (e.g. discarded) and optionally profiler 103 is used (in act 263 in FIG. 2A) to adjust (either automatically or under manual control) (1) the conditions (e.g. dosage of dopants) in unit 101 by driving a signal on a line 107 (FIG. 1A), or (2) the conditions (e.g. annealing temperature) in annealer 102 by driving a signal on line 108, or both. Then the above-described acts and acts are again repeated (as illustrated by branch 275).

Profiler 103 can perform an alignment at any time (e.g. after identifying a wafer as accepted/rejected as shown by act 270 in FIG. 2A). In one embodiment, profiler 103 includes two piezoelectric actuators that control the positions of beams 151 and 152. Specifically, the actuators (not shown) move a collimating lens of a laser that generates probe beam 152 along each of two orthogonal axes x, y that are both perpendicular to axis 155 of generation beam 151, thereby shifting the position of probe beam 152 relative to generation beam 151.

In this particular embodiment, profiler 103 aligns (see act 270 in FIG. 2A) beams 151 and 152 to be coincident in the following manner. Specifically, profiler 103 repeatedly moves probe beam 152 relative to probe beam 151 along an axis (e.g. along x axis), as illustrated in FIGS. 1F and 1G and obtains an intensity measurements after each movement. Thereafter, profiler 103 optionally plots the intensity measurements as a function of the relative position as illustrated in FIG. 1D, and determines the position (in this embodiment the voltage applied to the piezoelectric actuator) at which the intensity measurement is at a maximum, e.g. 25 volts in FIG. 1D.

In one embodiment, profiler 103 moves (see act 271 in FIG. 2C) probe beam 152 relative to generation beam 151 in a first direction (e.g. along the positive x axis) by an incremental distance Δx (e.g. 0.1 μm), measures (see act 272) if the measured intensity is larger than the largest intensity so far, and if so, saves (see act 274) the voltage signal that was used to maintain the current total distance between beams 151 and 152 and also saves the measured intensity as the largest intensity. Thereafter, profiler 103 repeats acts 271-274 until the total distance between beams 151 and 152 will exceed a predetermined distance, e.g. ½ of the diameter of the larger of beams 151 and 152, wherein the incremental distance Δx is {fraction (1/10)} of the larger diameter.

Next, profiler 103 moves probe beam 152 relative to generation beam 151 in a second direction (e.g. along the negative x axis) that is opposite to the first direction, and performs acts 271-274. Profiler 103 uses the value of the largest intensity from the previous performance of acts 271-274 during act 273 in the second direction performed for the first time—e.g. treats the negative and positive x axis travel to be a continuum and so obtains the voltage signal of 25 volts (FIG. 1D) corresponding to the maximum intensity measurement along x axis.

Similarly, profiler 103 moves probe beam 152 relative to generation beam 151 along another axis (e.g. y axis) that is orthogonal to the just-described movement, and once again determines the voltage applied to the piezoelectric actuator at which the intensity measurement is maximum, e.g. 40 volts in FIG. 1E. Therefore, profiler 103 automatically connects drift in optical alignment by performing act 270.

Thereafter, profiler 103 uses the just-described voltage levels to align the two beams, thereby to ensure that beams 151 and 152 remain coincident in the next set of measurements. Profiler 103 performs such alignment of beams 151 and 152 as often as required to obtain intensity measurements within the accuracy required by the system, e.g. once every N measurements (e.g. if profiler 103 is known to maintain alignment within the required accuracy for N measurements). In one particular example, the number of movements N between two acts of alignment is 1000.

As described below, the measurement performed by profiler 103 is non-destructive, is performed in a few square microns, and can be performed in a relatively short time (e.g. five seconds in one region or 50 seconds at 10 regions over a wafer). Measuring a property of annealed wafer 106 during (or immediately after) fabrication as described herein increases yield, as compared to an off-line measurement of a test wafer's properties.

Prior to measuring a material property by performing act 240, profiler 103 creates (see act 230 in FIG. 2A), in a region 120 (also called “illuminated region”) of wafer 106, a concentration n_(e) of excess carriers, and modulates concentration n_(e) (i.e. increases and decreases) as a function of time t but not as a function of distance x from a central axis 155 (FIG. 1C) of region 120. Specifically, over a time period that is the inverse of the modulation frequency, profiler 103 changes concentration n_(e) between the values n_(ea)-n_(en), wherein n_(en)≦n_(ej≦n) _(ei)≦n_(ea) (FIG. 1B). Therefore, at any given time ti, the value n_(ei) of the carrier concentration in semiconductor material 156 decays as a function of the distance x, without the creation of a wave in space. Profiler 103 ensures that there is no periodicity in space of the value of concentration n_(e). Instead, concentration n_(e) simply decays radially (e.g. roughly exponentially as a function of radial distance) outside region 120, as illustrated in FIG. 1B.

To ensure the absence of a wave in space, the frequency of modulation of carrier concentration C is selected to be several times (e.g. one or more orders of magnitude) smaller than the modulation frequencies used in the prior art to generate waves as described in, for example, U.S. Pat. No. 4,854,710. Specifically, in one implementation of this invention, the modulation frequency is approximately 1 KHz that is one thousand times (three orders of magnitude) smaller than a 1 MHz frequency described in column 15, line 18 of U.S. Pat. No. 4,854,710 by Opsal. Use of such a low modulation frequency is a critical aspect in one embodiment, and leads to unexpected results due to the elimination of a wave in space, such as the “wave” described by Opsal. In another embodiment, the modulation frequency is any frequency lower than 1000 Khz (e.g. 900 Khz) and profiler 103 still provides a measure of a material property as described herein.

In one embodiment, profiler 103 implements the above-described act 230 (FIG. 2A) by: generating (act 231 in FIG. 2B) a beam 151 (FIG. 1C) of photons that have energy greater than the bandgap energy of the semiconductor material in doped region 130, modulating (act 232 in FIG. 2B) beam 151 at a frequency selected to avoid the creation of a wave (as described above), and focusing (act 233 in FIG. 2B) beam 151 on doped region 130.

Depending on the implementation, profiler 103 modulates the intensity of generation beam 151 at any frequency in the range of 1 Hz to 20,000 Hz, as described below in reference to FIG. 4B. The modulation frequency can be, for example, 1000 Hz, and may require at least 10 cycles for a lock-in amplifier to generate a reflectance measurement (based on a probe beam as described below in reference to act 242), or 10 milliseconds to perform each reflectance measurement. In one example, the throughput is 30 wafers per hour, or 120 seconds per wafer, with each wafer having a measurement taken in at least ten regions.

If a material property measurement requires several reflectance measurements (e.g. a single region 120 requires a number of reflectance measurements for each of a corresponding number of average carrier concentrations), profiler 103 takes several seconds (e.g. 10 seconds) for each wafer 104/105/106. Hence, the 10 millisecond speed of reflectance measurement per region allows for real time control in the fabrication of wafers by apparatus 100 (FIG. 1A) using method 200 (FIG. 2A).

In another implementation of act 230, instead of using beam 151 of photons, profiler 103 uses a beam of charged particles, such as electrons or ions. The beam of charged particles is modulated and focused in the same manner as that described above in reference to beam 151 to generate the charge carriers in doped region 130. Instead of a beam of photons or a beam of electrons, any other mechanism (such as a combination of photons and electrons) can be used to create charge carriers in act 230 (FIG. 2A).

In act 240, one implementation of profiler 103 focuses (see act 242 in FIG. 2A) on a region (also called “illuminated region”) 120 illuminated by beam 151, another beam 152 (FIG. 1C) that is used to detect the number of charge carriers in wafer 104/105/106 when illuminated by beam 151. In one embodiment, beam 152 (also called “probe beam”) contains photons having energy lower than the bandgap energy of the semiconductor material in illuminated region 120. Such a probe beam 152 avoids the creation of measurement-related carriers when beam 152 is incident on illuminated region 120, thereby to maintain the charge carrier concentration the same prior to and during measurement (see act 243 in FIG. 2A) of a property as described below.

Next, profiler 103 measures (see act 243 in FIG. 2A) the intensity of a reflected portion of beam 152 (FIG. 1C) that is modulated at the frequency of modulation of the charge carriers in illuminated region 120. The intensity measurement provides an indication of an average concentration n_(av) of charge carriers in doped region 130 near surface 153, wherein the average concentration n_(av) is a root mean square average that is measured over the period of one (or more) modulation cycle(s) at the modulation frequency of generation beam 151. Concentration n_(av) in turn indicates, under certain conditions as discussed below, a material property, e.g. the mobility of charge carriers in doped region 130. Each intensity measurement is a measure of reflectance if the power of generation beam 151 is unity (e.g. 1 watt).

Although in FIG. 1C, beams 151 and 152 are illustrated as being coincident, with a common axis 155, in another embodiment, one of the beams, e.g. probe beam 152, is displaced with respect to the other beam to obtain an intensity measurement, e.g. location of generation beam 151 is changed on performance of one variant of act 244 (FIG. 2A). So beams 151 and 152 are separated each from the other as illustrated by a non-zero distance Δx between the respective axes 162 and 161 in FIG. 1F.

An intensity measurement obtained in such an offset position (FIG. 1F) of probe beam 152 with respect to generation beam 151 is used to measure various properties of the semiconductor material in doped region 130 a manner similar to the measurements obtained from coincident beams (FIG. 1C). The measurement obtained in the offset position (FIG. 1F) provides a measure of carrier concentration, because the concentration decays with distance d from illuminated region 120. Determination of lifetime from an intensity measurement in the offset position and another intensity measurement in the coincident position (FIG. 1C) is described below in reference to FIG. 7B.

In another embodiment, probe beam 152 is larger in diameter than generation beam 151 (as illustrated in FIG. 1H) due either to the difference in wavelengths of beams 151 and 152 or to properties of the beams such as the diameter and angle of divergence from a central axis. Specifically, probe beam 152 has a longer wavelength than generation beam 151, to ensure that the rate (also called “generation rate”) of generation of carriers due to probe beam 152 is significantly less than the generation rate due to generation beam 151.

As the diameter of a beam generated by a lens scales linearly with wavelength, when both beams 151 and 152 use lenses of the same diameter, the diameter of probe beam 152 at surface 153 is larger than the diameter of generation beam 151 as illustrated in FIG. 1C. The just-described larger diameter of probe beam 152 simplifies the alignment required to fully overlay generation beam 151 with probe beam 152, as compared to the alignment of beams having the same diameter.

In one embodiment, the diameter of probe beam 152 is made larger (see act 244 in FIG. 2A) than that required to obtain the above-described difference in the rate of carrier generation, e.g. 2 to 50 times the diameter of generation beam 151. As the diameter of probe beam 152 is increased, the reflected portion of probe beam 152 becomes more sensitive to the radial decay of carrier concentration 158 outside illuminated region 120, as shown in FIG. 1B. According to one aspect of the invention, the change in the rate of decay provides a measure of the degradation of carrier lifetime, as described below in reference to FIGS. 7A and 7B. Examples of intensity measurements generated with such a configuration of beams 151 and 152 are illustrated by points 502A-502N in FIG. 5A.

In one implementation, probe beam 152 has an initial diameter Dp that is approximately the same diameter Dl of lens 815 (described below in reference to FIG. 8A), and generation beam 151 has an initial diameter Dg that is sufficiently large to ensure that radius Wg (FIG. 1C) of generation beam 151 at surface 153 is larger than (or approximately equal to) the radius Wp of probe beam 152 (at surface 153).

In another embodiment, probe beam 152 has a diameter that is smaller than or equal to the diameter of generation beam 151 and is used to eliminate the effect of lifetime variations on the measurements of mobility and doping concentration (as described herein). The smaller size of probe beam 152 is achieved (as illustrated in FIG. 1C) by enlarging the diameter and/or the divergence angle of generation beam 151, e.g. by moving a lens used to generate beam 151.

Instead of changing a parameter used in the intensity measurements (as described above in reference to act 244), profiler 103 can change a parameter used in the creation of charge carriers in illuminated region 120 (see act 147 in FIG. 2A) to obtain a number of intensity measurements (see act 243). For example, profiler 103 can change the rate of carrier generation in region 120 by changing either the power of generation beam 151 (while holding all other parameters constant), or the diameter of generation beam 151 (while holding other parameters, e.g. power) constant, as described below in reference to FIG. 7A. Alternatively, profiler 103 can change the location of illuminated region 120 and perform a number of intensity measurements.

Profiler 103 can also change both parameters, namely the parameter used in creating the charge carriers as well as the parameter used in measuring the concentration of charge carriers (e.g. by performing each of acts 241 and 244), as would be evident to a person skilled in semiconductor physics in view of the disclosure. In one implementation discussed below in reference to FIG. 2C, the locations of each of probe beam 152 and generation beam 151 are changed to obtain a linear scan across a wafer 104/105/106, while holding the beams 151 and 152 coincident each with the other.

Although in the above-described embodiments, a probe beam 152 having photons of energy below the bandgap energy of wafer 156 is used (to avoid the creation of measurement-related carriers during the measurement), in another embodiment a small percentage of charge carriers in addition to the charge carriers created by generation beam 151 are created by use of a probe beam 152 (same reference numeral is used for convenience) having photons of energy at or slightly above the bandgap energy. The measurement-related carriers created by such a probe beam 152 are in a sufficiently small percentage (e.g. an order of magnitude smaller than the number created by the generating beam) to provide a reasonably accurate measurement of reflectance (e.g. to within 5%). Note that the overall accuracy of a measurement as described herein is also governed by other inaccuracies involved in the act of measuring, e.g. inaccuracies in a measurement device, such as an amplitude detector 818.

Therefore, in one embodiment the inaccuracy caused by the measurement-related carriers is kept only as small as necessary to maintain the overall accuracy below a predetermined limit. Specifically, the percentage of measurement-related carriers is kept sufficiently small when the rate per unit volume of the carriers generated by generation beam 151 (obtained by dividing the photon flux per unit area by the absorption length), is at least one order of magnitude (or more) larger than for probe beam 152.

The photon flux per unit area described above is the number of photons per unit energy obtained by dividing the power P of generation beam 151 by the area (πW₀ ²) of illumination by Plank's constant h and the ratio of the speed c of light to the wavelength λ as shown in the following formula: photon flux=(P/πW₀ ²) (1/h(c/λ)). The absorption length is the depth from surface 153 at which the intensity of generation beam 151 drops to (1/e) of the intensity at surface 153 (see equation 23).

In one implementation, the intensities of beams 151 and 152 are kept approximately equal (e.g. 100 milliwatts per cm²), and the number of charge carriers (also called “measurement-related carriers”) created by beam 152 is less than 10% of the number of charge carriers (also called “excess carriers”) that are created by generation beam 151 due to the difference in absorption lengths. Instead of intensities, the powers of beams 151 and 152 can be kept identical in case of an undoped layer of a wafer 104 because the dependence of carrier concentration on the diameter of beams 151 and 152 drops out as described below in reference to equation (5).

Note that in other implementations, beams 151 and 152 can have powers different from each other (e.g. 100 milliwatts and 25 milliwatts respectively), and yet maintain the number of measurement-related carriers at a negligible percentage. For example, probe beam 152 can have photons of energy greater than the bandgap energy, if the power of probe beam 152 is sufficiently less than the power of generation beam 151 (to keep the measurement-related carriers at a negligible percentage).

In one implementation, probe beam 152 has a generation rate one or more orders of magnitude smaller than the generation rate of generation beam 151. As noted above, the difference in generation rates is obtained by using beams 151 and 152 that have different absorption lengths in the semiconductor material of wafer 156, or by generating beams 151 and 152 at different powers or different diameters, or all of the above. In various implementations, the pair of beams 151 and 152 are generated by one of the following pairs of lasers: (AlGas, InGaAs), (Ar, InGaAs), (NdiYAG, InGaAs), and (NdiYAG, AlGaAs).

In one or more of the implementations, e.g. for use of lasers (NdiYAG, AlGaAs), the power of probe beam's laser (e.g. AlGaAs) is maintained less than the power of generation beam's laser (e.g. NdiYAG) because the absorption length of the probe beam is a fraction (e.g. one-tenth) of the absorption length of the generation beam. In another example, a probe beam 152 formed by a HeNe laser is maintained at a power less than or equal to ¼^(th) power of generation beam 151 formed by an Ar laser (having an absorption length 1.2 μm that is ¼^(th) the 3.0 μm length of the HeNe laser beam). In the just-described implementation, the power of the reflected portion of probe beam 152 is maintained large enough (by having a sufficiently large power of probe beam 152) to be detected with sufficient accuracy (e.g. with error of 5% or less) required for reflectance measurements as described herein.

In one variant of this implementation, the difference between the generation rates of beams 151 and 152 is one order of magnitude only at surface 153 (FIG. 1C). In a second variant, the order of magnitude difference is maintained throughout junction depth “Xj” of doped region 130 in wafer 105/106, e.g. throughout depth of 0.3 microns. In a third variant, the order of magnitude difference is maintained throughout a predetermined fraction (e.g. ½) of the junction depth Xj.

In one embodiment, the above-described intensity measurement obtained in act 243 is used directly to detect electrically active defects that could lie at various depths d near (e.g. within 1-2 μm) surface 153 (FIG. 1C) in wafer 105. Specifically variations in intensity measurements across a wafer 105/106 are detected by changing (as illustrated by act 247 in FIG. 2A) the region 130 illuminated by beams 151 and 152, and repeating the measurement in the new region. Note that beams 151 and 152 remain coincident (as illustrated in FIG. 1C and unlike FIG. 1D) when focused on the new region.

In a first embodiment, (also called “scanning embodiment”), the measured intensity is plotted (in a graph) along the y axis, as a function of position along the x axis (see FIG. 3A), in response to movement of coincident beams 151 and 152 across wafer 105/106, to determine if wafer 105/106 is within the specifications (as illustrated by act 260 in FIG. 2A). In one implementation, computer 103C displays on a monitor 103M (FIG. 1A) various graphs for either a linear scan (as illustrated in FIG. 3A) or an area scan (as illustrated in FIG. 3B).

Specifically, lines 370, 380 and 390 in FIG. 3A illustrate the measured intensity in microvolts as a function of position in microns, over a 20 micron movement of the following wafers (not shown): (1) a first wafer that has not been patterned generates line 380 that is used to characterize rapid thermal anneals, (2) a second wafer that was pre-amorphized with a high energy silicon implant (e.g. a uniform dose of 5×10¹⁴ silicon atoms per square centimeter at an energy of 100 Kev to cause uniform damage, and annealed at 1000° C. for 10 seconds to remove sub-surface defects) generates line 370, and (3) a third wafer having a uniform epitaxial region (e.g. grown with a thickness of 4 microns and a doping concentration of 1×10¹⁵ boron atoms per cubic centimeter) generates line 390.

As seen from FIG. 3A, the intensity measurement varies as a function of the expected defect level. The empirical data in FIG. 3A is explained below in reference to equation (12a). Specifically, the carrier concentration (indicated by an intensity measurement) drops when the lifetime drops due to a defect in a wafer 104 that does not have a junction. The analysis for a wafer 105/106 having a junction is similar, although requiring a more complicated analytical solution. Instead of such an analytical solution, a numerical model is prepared, in one implementation using Atlas software in computer 103C as described below.

Specifically, the defect level is expected to be highest on the first wafer (see line 380 in FIG. 3A), because the first wafer is the lowest quality wafer among the just-described three wafers. Line 380 has the largest variation (as compared to lines 370 and 390), with defects at each of valleys 380A-380P (where A≦I≦P, P being the number of valleys, in this example P=8).

The second wafer with an annealed silicon implant is expected (due to the anneal) to have less defects, and as illustrated by line 370 has less variation than line 380 and fewer valleys 310A-310P (where P=5 in this example). The lowest defect level is expected in the third wafer since an epitaxial wafer includes a pure silicon crystal layer at the surface, so that the surface has no residual polishing damage. As illustrated by line 390, small sized (e.g. with a dimension <100 ↑) defects near (within a depth of 1-2 μm from surface 153 in FIG. 1C) have electrical activity (wherein such defects act as sites for charge carriers of opposite polarity to recombine, thus reducing the lifetime) that causes a small variation (as illustrated in FIG. 3A) in the intensity measurements.

In one implementation, a ratio (also referred to as “peak-valley” ratio) is determined by dividing the signal value at a peak (i.e. a local maximum, e.g. peak 372 having a signal value of Sh1) by the signal value at a valley (i.e. a local minimum, e.g. valley 370A having a signal value of Sl1), to obtain a ratio e.g. Sh1/Sl1 for line 370 (and similarly ratio Sh2/Sl2 for line 380 and ratio Sh3/Sl3 for line 390). Thereafter, the ratios for wafers undergoing the same fabrication process, if smaller than or equal to a predetermined ratio identify acceptable wafers. For example, if ratio (Sh1/Sl1) of wafer 105/106 is greater than the predetermined ratio (Shm/Slm) as illustrated in FIG. 3A, wafer 1015/106 is identified as unacceptable (e.g. by placing in a bin of rejected wafers).

In one implementation, computer 103C displays on monitor 103M a message indicating that measurements identify a wafer 104/105/106 as unacceptable, while in another implementation computer 103C drives a signal to a robot (not shown) to move wafer 104/105/106 into a bin of rejected wafers (if rejected). The acceptable wafers are processed further in the normal manner (see act 262 in FIG. 2A).

A predetermined ratio (Shm/Slm) is set empirically by comparing the above-described ratios of one or more reference wafers (wherein the reference wafers are known to be good or bad based on electrical tests for conformance to the specification for such wafers), thereby to identify a maximum limit on the ratio for acceptable wafers. The empirical method used can be any method such as one of the methods described in “STATISTICAL QUALITY CONTROL HANDBOOK” available from AT&T Technologies, Commercial Sales Clerk, Select Code 700-444, P.O. Box 19901, Indianapolis, Ind. 46219, phone 1-800-432-6600, second edition, 1958.

Specifically, the variations in such a peak-valley ratio are correlated with the performance of a reference wafer during electrical tests that identify reference wafers (that are good). In one example, four different wafers have 1%, 5%, 10% and 20% variation from the peak-valley ratio Sh3/Sl3 (e.g. ratio 1.2) of an epitaxial wafer, and have the respective variations in performance speed of 8%, 10%, 20% and 25% during electrical testing of integrated circuit dies formed from the respective wafers.

Assuming that 10% and greater variation in speed is unacceptable, the predetermined ratio is set for this example at 5% variation. Therefore, all wafers having variation of peak-valley ratio lower than 5% are identified as acceptable wafers (as illustrated by act 262 in FIG. 2A). Note that if the peak-valley ratios of a number of wafers that have been successively processed are close to the predetermined ratio (e.g. all greater than 4.5% in the just-described example), one or more parameters used in processing the wafers may be adjusted (e.g. as described herein in reference to act 263 of FIG. 2A) even though none of the wafers are discarded.

In another implementation, instead of computing a ratio and comparing the ratio to a predetermined limit, a difference (also called “measured difference”) Sh1-Sl1 Sl1 between local maximum 372 and local minimum 371, is compared directly with a predetermined limit Shm-Slm on such a difference, and the number of times the measured difference (over a unit distance) exceeds the predetermined limit is used as an indication of the number of defects in the wafer. The number of defects in wafers that have been annealed are detected(e.g. as valleys 380A-380P in FIG. 3A), and compared with a predetermined limit (e.g. 0 defects)on the number of defects, to accept or reject a wafer. In one implementation, computer 103C displays a message indicating the number of defects on monitor 103M.

In still another implementation, each measured intensity for a wafer 104/105/106 is compared with a predetermined range (e.g. the range Shm-Slm in FIG. 3A), and if any intensity falls outside the range, the wafer is rejected. Therefore in one example, if two wafers represented by lines 380 and 390 are formed by the same process, the wafer represented by line 380 is rejected and the wafer represented by line 390 is accepted.

Moreover, defects in an annealed wafer 106 cause changes in the shape of a plot of the measured intensity vs. power of the generation beam (see FIG. 3A described below). Therefore, in one embodiment, after identifying the locations of defects (e.g. the x-coordinate of each valley 380A-380N in FIG. 3A), a number of intensity measurements are performed at each location, and used to obtain a material property or process condition at the location.

Such material properties are of interest in the processing of wafers because of the sensitivity of reflectance measurements as described herein to the removal or creation of defects by processes such as annealing. Specifically, when the above-described act 240 (FIG. 2A) is performed on a wafer 104 before processing in wafer processing unit 101 (FIG. 1A), defective wafers are screened out at the beginning, i.e. prior to any processing as described herein (e.g. formation of doped regions), thereby eliminating two types of defects: (1) defects in a wafer caused by polishing and (2) defects in epitaxial material. Moreover, when act 240 is performed on a wafer 105/106, any defects caused by a fabrication process (e.g. ion implantation, annealing, etching or patterning) is identified (as described herein).

In addition, act 240 is used in one implementation to screen out starting wafers formed of bare silicon. When defects in such bare silicon are identified at the beginning, the method results in correction of the wafer fabrication process to ensure a sufficiently low defect level and eliminate the cost and use of a starting wafer 106 formed of epitaxial material. Starting wafers formed of pure silicon (also called “prime wafers”) are processed by profiler 103 in a manner identical to starting wafer 104 as described herein.

Anneals are typically done by heating the wafer rapidly with lamps (not shown) in annealer 102 (FIG. 1A). The illumination by the lamps in annealer 102 may not be uniform, and the amount of heat that enters a patterned wafer 105 at any point may be a function of the thickness of dielectric layers (such as silicon dioxide or silicon nitride to be formed on surface 153), and the integrated circuit pattern therein. Specifically, the different layers (not shown) in wafer 105 reflect different amounts of power, thereby causing variations in the amount of heating of wafer 105.

Thus annealing of implanted wafer 105 may not be uniform, and the characteristics of a junction (formed at an interface between doped region 130 and semiconductor material 156 in FIG. 1C at a depth xj from surface 153) in annealed wafer 106 may vary from point-to-point. Lines 370, 380 and 390 (FIG. 3A) indicate to a person skilled in semiconductor physics the variations in junction properties on a micron and sub-micron scale. Therefore, such lines are used by a human operator of profiler 103 to check if the just-formed transistors are uniform all across wafer 105/106, and to conform to specifications (e.g. by adjusting the anneal, implant or circuitry design) the transistors in a to-be-formed wafer.

Instead of a human operator, such checking is automated by computer 103C in another embodiment. For example, instead of forming a display (as shown in FIGS. 3A and 3B), computer 103C (1) automatically uses the measurements of each wafer to compute the mean and standard deviation values, over a large number of wafers (typically several hundred or more), and (2) automatically uses these values of mean and standard deviation to identify when an implant or anneal process is out of specification, using statistical process control methods that generate control parameters (as described in pages 5-30 of the above-referenced book from AT&T Technologies, and these pages are incorporated by reference herein) to be provided to unit 101 or annealer 102.

As noted above, although a linear scan is illustrated in FIG. 3A, an area scan is performed in another embodiment as illustrated in FIG. 3B. Specifically, profiler 103 (FIG. 1A) performs a number of reflectance measurements in a corresponding number of regions (e.g. by repeating acts 244 and 243 in FIG. 2A) in a closely spaced grid (e.g. a grid that divides a wafer 105/106 into a number of regions, each region having an area 10 microns by 10 microns). The reflectance measurements are plotted to form on monitor 103M (FIG. 1A) a graph of the measured intensity vs. x-y position (e.g. in the form of various types of hatched regions as shown in FIG. 3B or preferably as a three dimensional image). Thereafter the graph of the area scan is used by an engineer skilled in semiconductor physics to evaluate wafer 105/106, in a manner similar to the the use of a scanning electron microscope.

Instead of plotting a graph to be manually checked, the reflectance measurements are checked automatically in another implementation, using statistical process control methods as described above. Also, each reflectance measurement obtained by act 243 (FIG. 2A) provides an indication of a material property (e.g. the mobility of charge carriers) in wafer 105/106 (FIG. 1A). Specifically, profiler 103 is programmed to obtain a number of measurements (in at least one region 301) that are used (as described below in reference to FIGS. 5A-5H) to calibrate a measurement with respect to the material property (e.g. obtain a sealing factor to convert a reflectance measurement into doping concentration or a slope from a number of measurements into mobility).

In one implementation, profiler 103 performs a group of measurements (e.g. at least two measurements for two different powers of generation beam 151) in each region of wafer 105/106. Therefore in the just-described embodiment, profiler 103 functions as a scanning mobility microscope that displays on monitor 103M the mobility of various regions on wafer 104/105/106, and can be used in a manner similar to the use of a scanning electron microscope. In one example, four hundred measurements are taken in an area of 100 μm×100 μm and displayed in a three dimensional graph wherein the x and y axes define, in the two dimensions, a region on patterned wafer 105, and the hatch pattern (that is displayed on monitor 103M in a third dimension) indicates the measured reflectance.

In another embodiment, the location at which the charge carriers are created is not changed between two or more measurements. Instead, in performing act 241 (FIG. 2A), profiler 103 (FIG. 1A) creates charge carriers in the same location, and changes a parameter used to create the charge carriers. The parameter can be, for example, the average carrier concentration nav in region 120. Concentration nav is changed e.g. by changing the intensity of generation beam 151 (e.g. by changing the power or the diameter), as described below in reference to FIG. 5A.

Also, instead of or in addition to act 241, profiler 103 changes a parameter used in the measurement as illustrated by act 244 in FIG. 2A, e.g. changes the diameter of probe beam 152 or changes the location at which the reflectance is measured by offsetting the position of beam 152 relative to beam 151, as described above in reference to FIG. 1F.

In one embodiment, two or more of the reflectance measurements made in act 243 (FIG. 2A) are used to measure a material property of wafer 104/105/106 by one or more acts 451-455 (FIG. 4A). Specifically, in act 451, profiler 103 fits the reflectance measurements to a line, such as curved line 471 (FIG. 4B). Curved line 471 is a plot (along the y axis) of the intensity of probe beam 152 (FIG. 1C) after reflection by region 120, as a function of the parameter being varied (along the x axis), e.g. power of generation beam 151 incident on region 120. Profiler 103 (FIG. 1A) uses points 471A-471N obtained by each of the intensity measurements to fit a curved line 471 (FIG. 4B) for a wafer (e.g. by connecting points 471A-471N with line segments).

Next, in act 252 (FIG. 4A), profiler 103 determines one or more attributes that describe curved line 471, e.g., determines the first order coefficient (also called “slope”) and the zeroth order coefficient (also called “intercept”) of one or more straight lines that approximate various portions (e.g. two portions described below) of curved line 471, and/or determines an inflection point (e.g. a point at which a second or higher order derivative becomes zero). In the example illustrated in FIG. 4B, curved line 471 has a point (hereinafter “inflection point”) at which the slope changes in such a manner as to allow a majority (greater than 50%) of the intensity measurements greater than the measurement at inflection point IP to be approximated by a straight line 471H. Similarly, a majority of the intensity measurements below the measurement at inflection point IP are approximated by another straight line 471L.

So curved line 471 has a high-power portion HP that corresponds to a condition called “high level injection” wherein the concentration of excess carriers created by generation beam 151 (FIG. 1C) is greater than the concentration of background charge carrier normally present in doped region 130 due to activated dopants. Line 471 also has a low power portion LP that represents a condition called “low level injection” wherein for powers of generation beam 151 lower than powers in portion HP, the rate of generation of excess carriers in doped region 130 is smaller than the concentration of background charge carriers due to the activated dopants. Low power portion LP and high power portion HP are each separated from the other by the just-described inflection point IP.

Lines 471H and 471L are obtained by computer 103C (FIG. 1A) without knowledge of inflection point IP by using two or more of the intensity measurements at the extreme ends of the range of measurements. For example, two points 471A and 471B that represent the highest intensity measurement and the next highest intensity measurement can be used to determine line 471H, while two other measurements 471N and 471M that represent the lowest intensity measurement and the next lowest intensity measurement are used (by computer 103C) to determine line 471L. Instead of using two points, in another embodiment three adjacent points at the high end of the range, e.g. points 471A-471C, are used to obtain a best fit line 471H, while three adjacent points 471K-471N at the low end of the range are used to obtain the best fit line 471L. In one implementation, inflection point 471I is found from the just-described lines 471L and 471H, as the point on curve line 471 that is the closest to an intersection point of lines 471L and 471H.

As noted above, in FIG. 4B the parameter varied in act 244 or act 247 (FIG. 2A) is plotted along the x axis. Therefore, depending on the implementation, the intensity measurement (see y axis) is plotted against one of the following: the power of generation beam 151 (as illustrated in FIG. 5A), the parameter of probe beam 152 (as illustrated in FIG. 7A), and the offset distance between beams 151 and 152 (as illustrated in FIG. 7B).

Although a pair of straight lines 471L and 471H are used to approximate curved line 471 in one implementation, other implementations use other numbers of straight lines (e.g. a single straight line for the entire curved line 471, or three or more straight lines). In alternative implementations, instead of using straight lines, computer 103C uses quadratic or higher order functions that approximate curved line 471, e.g. to obtain three or more such coefficients.

In one implementation, programmed computer 103C generates a number of curved lines 501-504 (FIG. 5A) from intensity measurements on four different wafers. For example, profiler 103 obtains a number of measurements 502A-502N with beams 151 and 152 coincident in the same region 120 (FIG. 1C) by changing the power of the generation beam 151. Thereafter, computer 103C generates lines 502H and 502L in the manner described above in reference to FIG. 4B, and thereafter determines the respective slopes m_(H) and m_(L), and the respective y intercepts YH and YL by performing acts 246A and 246B (FIG. 4A). In the just-described example, wafers represented by lines 501, 503, and 504 have known material properties, while the properties of a wafer represented by line 502 are unknown.

In one implementation, the properties and process conditions of wafers represented by lines 501, 503 and 504 are plotted as functions of one or more of the above-described coefficients, e.g. high power intercept YH and low power slope m_(L), as illustrated by FIGS. 5B, 5C, 5D and 5E. Thereafter, the corresponding coefficients of line 502 are used to look up the respective properties and/or processing conditions.

Specifically, in the example illustrated in FIG. 5A, curved lines 501-504 have the following fit coefficients shown in Table 1.

TABLE 1 Anneal Temperature in Line m_(L) m_(H) YL YH Degrees Centigrade 501 2.70 1.88 −13.9 20.6 950 502 4.05 1.89 −12.5 89.1 1000 503 4.13 2.92 −25.7 51.8 1050 504 1.94 2.52 −6.8 −49.5 900

Therefore, computer 103C uses the high power intercept YH of value 89.1 as illustrated in FIG. 5B to obtain the anneal temperature as 999° C. from line 510 that is obtained from the known anneal temperatures of each of wafers represented by lines 501, 503 and 504. Similarly, computer 103C uses the low power slope m_(L) of value 4.05 in FIG. 5C to obtain an anneal temperature of 1000° C. from line 309 again obtained from the known anneal temperatures. Although each of FIGS. 5B and 5C provide the same information for the wafer represented by line 302, i.e. an anneal temperature of around 999.5° C. (average of the two measurements obtained from FIGS. 5B and 5C), FIG. 5C is useful when FIG. 5B provides ambiguous information, e.g. indicates two anneal temperatures of 980° C. and 1040° C. when high power intercept is 60. The low power slope can be used to pick one of the two values 980° C. and 1040° C., e.g. pick 980° C. when the low power slope is less than 4.0.

In the above-described example of the wafer represented by curve line 302, programmed computer 103C compares the measured value of 999.5° C. with the specification of 975° C. (as illustrated by act 260 in FIG. 2A), and identifies the wafer as being rejected (e.g. by moving the wafer into a bin of rejected wafers), and thereafter adjusts a process parameter e.g. drives a signal on line 108 (FIG. 1A) to reduce the temperature by 25° C.

Instead of, or in addition to determining a process condition (e.g. anneal temperature as described above in reference to FIGS. 5B and 5C), the above-described attributes derived from the intensity measurements can be used to determine one or more properties of the semiconductor material in illuminated region 120. Specifically, profiler 103 uses the low power slope m_(L) to determine junction depth Xj (FIG. 1C) by looking up a graph (FIG. 5D) of such slopes plotted against junction depth of wafers having known properties. In the above-described example, the low power slope ML has a value of 4.05, and line 511 (FIG. 5D) yields a junction depth of 580 angstroms.

Thereafter, profiler 103 compares the value of 580 angstroms with a predetermined range of acceptable junction depths e.g. the range of 400 to 600 angstroms. As the value of 580 falls within the range, wafer 105/106 is identified as acceptable, and is processed further in the normal manner (as illustrated by act 262 in FIG. 2A). If the measured junction depth falls outside the predetermined range, wafer 105/106 is rejected (as illustrated by act 260 in FIG. 2A), and one or more process conditions are adjusted e.g. by adjusting the addition of dopants (as illustrated in act 263).

Note that the adjustment of a process condition can also be performed even when a wafer is accepted (as illustrated by act 262), e.g. if the measured property (such as the junction depth) falls closed to the limits of the range, e.g. within 5 percent of the limit (in the above-described example within the range of 400-408, or within the range of 475-500). As noted above, to adjust the process condition, profiler 103 provides a signal to either or both of unit 101 and annealer 202 to return the value of the measured property back to the middle of the predetermined range (e.g. to 500 angstroms).

Measuring junction depths as described above in reference to FIG. 5D provides an unexpected result, considering that at least one prior art reference, namely U.S. Pat. No. 4,854,710 granted to Opsal teaches that depth information cannot be obtained in the absence of a plasma wave (specifically, Opsal states in column 4, lines 33-35, “[h] owever, in applications where sample variations as a function of depth need to be studied, it is necessary to generate and study plasma waves”).

Similarly, profiler 103 uses another attribute, specifically the high power intercept YH to look up the concentration of active dopants at surface 153 (FIG. 1C). Specifically, profiler 103 uses the high power intercept YH of value 89.1 to obtain a surface concentration of 7×10⁹ atoms/cm³ from line 512 (FIG. 5E) formed by plotting the high power intercepts of a number of wafers having known surface concentrations.

Instead of, or in addition to the use of a coefficient (e.g. one of the above-described slopes or intercepts to measure the concentration of dopants at the surface (as discussed above in reference to FIG. 5E), profiler 103 can use another attribute of curved line 502, specifically an inflection point IP of line 502 at which the second or higher order differential close to zero. Specifically, in one implementation, profiler 103 uses the x coordinate XI of the inflection point IP to determine the power of generation beam 151 and uses another graph (FIG. 5F) to look up the concentration of active dopants in material 156 (FIG. 1C).

Curved line 514 (FIG. 5F) is used directly with the generation beam's power at the inflection point IP as determined from FIG. 5A to look up the doping concentration. For example, when the value of the x coordinate of the inflection point IP is 43, curve line 154 yields a value of 7×10¹⁹ atoms/cm³ value for the doping. Line 514 (FIG. 5F) is obtained by programming the Atlas software into computer 103C to form a simulator as described herein, and providing to the simulator information on the material structure (description of the doped layers) and generation beam 151 (description of diameter, power and wavelength), for various doping concentrations and various powers.

Sheet resistance Rs of region 130 (FIG. 1C) can also be determined from the high order slope m_(H) of line 502 (FIG. 5A) from a plot of the slope versus the sheet resistance as illustrated in FIG. 5G. Specifically, profiler 103 normalizes the measured slope to the slope of a wafer having a step junction, a 0.2 micrometer deep doped region 130, doped with 20 KeV implant into N-type epi wafer at a dose of 1×10¹⁵ atoms/cm³, with a probe beam 152 having a diameter 2 micrometers and power 41.5 μm, and generation beam 151 having a diameter 2 μm, and power varied from 0 to 90 mW.

Therefore, in one implementation, line 381 (FIG. 5G) is obtained by modeling the sheet resistance Rs using a finite element simulator, such as computer 103C (FIG. 1A) programmed with the software “Atlas” available from Silvaco of Sunnyvale, Calif. Such a simulator is set up (in a manner apparent to the skilled engineer in view of the disclosure) to model the carrier concentration at surface 153 (FIG. 1C) of semiconductor material 156 in response to illumination by generation beam 151, thereby to determine according to the model, a reflectance that is normalized with respect to the reflectance obtained from a wafer having a step junction 0.2 micrometer deep, and doped with 20 KeV implants into n-type epi on an n-type wafer.

The normalized reflectance is plotted as a function of the sheet resistance Rs to yield line 516, and the measured values are scaled (by normalization) to yield line 515 (FIG. 5G) coincident with line 516. Sheet resistance Rs varies inversely with each of doping concentration (FIG. 5F), and with junction depth Xj (FIG. 5D). Therefore, the junction depth Xj is held constant, by implanting with a constant energy while varying the dosage and therefore the doping concentration to create a variation in sheet resistance Rs.

The slope m_(H) of the high power portion HP (FIG. 4B) is proportional to inverse of the mobility, which is in turn proportional to doping concentration (as illustrated by the FIG. 6B). Therefore, the normalized high power slope m_(H) (described above) is sensitive to the sheet resistance Rs, as demonstrated both by experiment and the simulator (and shown in FIG. 5G).

Profiler 103 extracts sheet resistance Rs as follows. Specifically, profiler 103 measures, for a wafer having a known sheet resistance Rs, a high power slope m_(H) as described above (FIG. 5G) in the high power portion HP, e.g. such a reference wafer has sheet resistance of 500 ohms per square, thereby calibrating the slope value of 0.6. Thereafter, profiler 103 uses the calibrated value to plot the high power slopes against the sheet resistance, and obtain line 515.

Next, profiler 103 measures the reflected powers and determines a slope for a wafer with the same implant energy as the wafer having known properties used to calibrate lines 515 and 516. For example, the wafer with the unknown sheet resistance may have a slope of 0.8, and therefore profiler 103 determines the sheet resistance (from FIG. 5G) to be 1000 ohms/square.

For a step junction (a junction having one constant level of doping for depth values from the surface to the junction depth and a second constant level of doping for depth greater than the junction depth), the sheet resistance is given by $R_{s} = {\frac{\rho}{Xj} = \frac{1}{q\quad \mu \quad n\quad {Xj}}}$

where ρ is the resistivity, Xj is the junction depth, μ is the mobility, and n is the active carrier concentration. Thus, the sheet resistance Rs combines mobility, active doping concentration, and junction depth so that one of these can be determined from the others. For example, profiler 103 determines mobility using the above-described equation, after determining sheet resistance (from FIG. 5G), doping (from FIG. 5P) and junction depth (from FIG. 5D) as described above.

The high power slope m_(H) of a plot of intensity measurements as a function of the power of generation beam 151 (e.g. lines 501-504 in FIG. 5A) is used to obtain mobility by simply dividing slope (for high injection) with a corresponding slope of a reference wafer and multiplying by the known mobility as shown by the formula: $\mu_{unk} = {\frac{m_{ref}}{m_{unk}}\mu_{ref}}$

Specifically, for high-level injection, the current is radial as described below in reference to FIG. 9B. Therefore, the carrier concentration is given by equation (5) that is also described below. Combining equations (5), (21) and (22) described below gives the high power slope $m_{H} = {\frac{{q^{3}\left( {1 - R_{0}} \right)}\alpha}{2{\pi \left( {m_{0}^{2} - 1} \right)}\varepsilon_{0}\varepsilon_{s}m^{*}\omega^{2}{kTE}_{ph}}\left( \frac{1}{\mu} \right)}$

where m_(H) is the slope of the high power portion of the line obtained by plotting along the y axis the reflection signal normalized to the absolute reflection as a function of the generation beam 151's power plotted along the x axis, q is the electron charge, R₀ is the absolute reflection, α is the absorption coefficient, equal to the inverse of the absorption length m₀ is the index of refraction of the silicon, ε_(s) and ε₀ are the dielectric constants of free space and the silicon, m_(e) is the carrier effective mass, ω is the radial frequency of the probe beam, k is Boltzmann's constant, T is the temperature, and E_(ph) is the energy of one photon at the generation beam wavelength, and μ is the mobility.

A curve such as line 517 (FIG. 5H) is found from the above equation. In more complex situations, line 517 can be found by numerical modeling. Line 517 also can be found empirically by measuring m_(H) and correlating to mobilities measured, for example, by constructing transistors on the same material and measuring the mobility based on the performance characteristics of the transistor. Thereafter, profiler 103 uses the high power slope m_(H) of a wafer under fabrication to look up mobility using line 517.

Graphs, such as lines 509-513 in FIGS. 5B-5F, that are used to determine a material property or a process condition are generated in one of the two following ways (in two different embodiments). In the first embodiment, a set of wafers (also called “reference wafers”) is selected or prepared to have a range of material properties (by varying process conditions, such as implant energy, dose or anneal temperature), and thereafter profiler 103 is used to obtain intensity measurements and generate fit coefficients or other attributes for each of the reference wafers (as described above). Thereafter, the fit coefficients or attributes are used to plot lines 509-513 and 515. In a second embodiment, a number of wafers (also called “reference wafers”) are subjected to intensity measurements in profiler 103 (as described above), followed by use of a conventional measurement technique, such as spreading resistance profiling to determine the actual doping profile therein.

In one example, lines 501-504 in FIG. 5A represent wafers created by ion implantation at an energy of 2 KeV and dosage of 1×10¹⁵ using boron, followed by annealing at each of the following temperatures: 950° C. for line 501, 1000° C. for line 502, 1050° C. for line 503 and 900° C. for line 504. Thereafter, intensity measurements are obtained as described above, and plotted to form the graphs in FIG. 5A. Next, spreading resistance profiles (abbreviated as “SRP”) are prepared, as illustrated in FIG. 6A, wherein the reference numerals obtained by adding 100 to the reference numerals in FIG. 5A indicate lines corresponding to the same wafers (e.g. line 501 in FIG. 5A corresponds to line 601 in FIG. 6A).

SRP lines 601-604 illustrated in FIG. 6A, are prepared by breaking the wafers to expose the ion-implanted layer followed by beveled edging and probing to measure the profile of the concentration of active dopants as a function of depth. Therefore, at the end of the preparation of SRP, the graphs (FIG. 6A) provide a plot of the active dopant concentration (atoms/cm³) along the y axis as a function of depth (in microns) along the x axis. From lines 601-604, programmed computer 103C determines the surface concentrations 601Y-604Y, that are thereafter used to generate line 512 illustrated in FIG. 5E. Moreover, programmed computer 103C determines the depths at the dopant concentration value of 1×10¹⁹, specifically x coordinates of points 601J-604J, and uses these values to generate a plot of low power slope versus junction depth illustrated as line 511 in FIG. 5D. Straight lines generated by the above-described methods fit (in an act called “curve-fitting”) the measurements well, e.g. R² values of greater than 0.95 in FIGS. 5D and 5E.

Therefore, after one or more of the above-described graphs (see FIGS. 5B-5G) are prepared, the material properties of a wafer under fabrication are determined by the above-described method 200 (FIG. 2A) without the need to break and lap the wafer, because profiler 103 simply uses the above-described graphs to generate measurements of material properties. Therefore, profiler 103 eliminates the cost associated with test wafers otherwise required by the prior art methods (for breaking and lapping).

Although in the above description, computer 103C has been described as performing various computations for preparation of lines (e.g. line 512 in FIG. 5E) used to measure material properties, such graphs can be prepared by another computer, or alternatively can be prepared manually by performing the above-described acts.

Moreover, although in one embodiment the above-described lines (e.g. FIGS. 5A-5G) are prepared, in another embodiment such graphs are not prepared and instead the reflectance measurements are simply used to perform the various acts of method 200 by use of equations related to such graphs. For example, instead of drawing a line 512 (FIG. 5E), the slope and intercept of such a line are determined, and thereafter an equation containing the slope and intercept is used with the high power intercept to obtain the surface concentration.

Also, instead of line 512 being a straight line, a curved line can be used, and alternatively, a second or higher order differential equation can be fitted to the intensity measurements to obtain the property be apparent to a person skilled in the art of computer programming).

Furthermore, well known relationships, such as the relation of mobility to dopant concentration (as illustrated by line 611 in FIG. 6B) can be used in addition to (or instead of) the above-described graphs (in FIGS. 5B-5G). Specifically, in one embodiment, profiler 103 uses a line 611 (FIG. 6B) in the range of 10¹⁶ to 10¹⁹/cm³, a range that is in common use in integrated circuit processing, to obtain mobility of the value 100 centimeters per second from a dopant concentration of 4.2×10¹⁹ atoms/cm³ that is obtained as described above in reference to FIG. 5E. Note that although the surface concentration obtained from FIG. 5E is higher than the dopant concentration in the bulk, the mobility obtained from line 611 approximates the mobility in the bulk, because the mobility drops only slightly between 10¹⁹ and 10²⁰ atoms/cm³ dopings, as described below in reference to FIG. 9C.

Another well known relationship, illustrated by line 613 (FIG. 6C) can be used to estimate the bulk lifetime from a knowledge of the dopant concentration as follows. Specifically, profiler 103 uses the dopant concentration e.g. of value 4.2×10¹⁹ to lookup, from line 613, a bulk lifetime of value 1.1×10⁻⁵ milliseconds. The surface dopant concentration provides an estimate of the lifetime in the bulk material 156 (FIG. 1C).

Instead of using the known relationships (e.g. lines 611 and 613 in the respective FIGS. 6B and 6C), relationships specific to the wafers being fabricated can also be prepared as described above in reference to FIG. 5H from the appropriate measurements of the mobility and lifetime using conventional methods, and these relationships are thereafter used in profiler 103 to measure the mobility and lifetime of a wafer under fabrication as described herein.

The above-described known relationships (such as the relationship between mobility and dopant concentration described above in reference to FIG. 6B) provides an accurate estimate only in the absence of effects (such as surface roughness and dopant segregation) that reduce mobility. Specifically, surface roughness causes scattering that degrades the value of surface mobility to a level below bulk mobility, so that the surface mobility that determines line 502 (FIG. 5A) may not be the same as the bulk mobility corresponding to the carrier concentration that determines inflection point IP (FIG. 5A).

Therefore, one embodiment uses two attributes together to obtain a property e.g. (1) uses inflection point IP (as described above in reference to FIG. 5F) to obtain dopant concentration, and (2) uses line 502 (specifically the high power intercept YH) to obtain surface concentration (as described in reference to FIG. 5E) to determine a change in the doping concentration (independent of surface roughness). Specifically, the inflection point indicates a condition when the concentration of excess carriers equals the doping concentration. For example, if the surface mobility is half the bulk value, then a doping concentration extracted from a mobility of 100, using point 612 indicates a value of 4×10¹⁹, while a doping concentration extracted from the inflection point using FIG. 5F, indicates a value of 1×10¹⁸.

Instead of changing the power of generation beam 151 between reflectance measurements to generate lines 501-504 (FIG. 5A), another parameter can be changed as illustrated by act 244 described above in reference to FIG. 2A. Specifically, in one implementation, the diameter of either probe beam 152 or generation beam 151 is changed between reflectance measurements, and therefore yields measurements that are sensitive to the rate dn_(ei)/dx of carrier concentration 158 as shown in FIG. 1B. The change in rate n_(ei) is used to measure degradation of carrier lifetime as illustrated in FIGS. 7A and 7B.

Specifically, lines 701 and 702 (FIG. 7A) illustrate limits of a range of acceptable lifetimes of a wafer under fabrication, and represent along the y axis the normalized intensity measurement, plotted against the radius of probe beam 152 (FIG. 1H). The intensity measurement illustrated in FIG. 7A is normalized to the intensity measurement obtained by use of a probe beam 152 of the diameter 1 micrometer for no degradation in the lifetime, on a wafer 105/106 having a step junction 0.2 micrometer deep, doped with a p-type dopant at a dosage of 5×10¹⁸.

Therefore, profiler 103 simply plots point 703 in the graph of FIG. 7A from a measurement obtained for a wafer under fabrication, and checks to see if point 703 falls within a region 704 defined to be the acceptable region between limits 701 and 702. If so, profiler 103 decides that wafer 105/106 that generated measurement 703 has an acceptable lifetime. Note that the above-described measurement represented by point 703 is a single measurement, and therefore the single measurement is adequate to decide the acceptance or rejection of a wafer as described herein.

Moreover, in one implementation, a number of additional lines, e.g. lines 700I and 700J are included, and profiler 103 estimates the lifetime at point 703 by interpolation, e.g. to be 500 times degraded (because point 703 falls between line 700I for 100 times degradation and line 700J for 1000 times degradation). A plot of the normalized intensity measurement versus the probe beam diameter provides an accurate test for checking the lifetime of a wafer 105/106, because the intensity measurement is linearly proportional to the concentration of carriers generated by generation beam 151 at surface 153, as illustrated by lines 711 and 712 (FIG. 7B) corresponding to the above-described lines 701 and 702.

Note that in FIG. 7B, the x axis indicates radial distance from axis 155 (FIG. 1H) of generation beam 151. The relationship between intensity measurement and the surface concentration is described below in reference to equations 21 and 22. Note that in view of equations 21 and 22, instead of a reflectance measurement being used to measure a property of the semiconductor material, a change in the index of refraction can also be used in a similar manner.

In one implementation, beam 152 (FIG. 1C) is a laser beam having a wavelength greater than 1 μm (the wavelength at which photons have approximately the same energy as the bandgap energy of silicon). Note that the wavelength of beam 152 depends on the bandgap energy and therefore on the specific material in wafer 105/106, and is different for germanium.

In one example, probe beam 152 is generated by a laser 801 (FIG. 8A), such as a 1480 nm fiber coupled laser diode, model CQF756/D having a maximum output power of 70 milliwatts, available from Philips Corporation, Eindhoven, The Netherlands. Laser 801 is mounted separate from other components in profiler 103, and is coupled to a collimator 803 by a fiber 802 that carries beam 152. Collimator 803 can be, for example, part number WT-CY3-163-10B-0.5 available from Wave Optics, Mountain View, Calif.

In this implementation, generation beam 151 is created by an above bandgap laser 805, such as 830 nm laser diode model SDL-5432-H1 having a maximum output power of 200 milliwatts, available from Spectra Diode Labs, San Jose, Calif. Profiler 103 includes a lens 806, which is part number 06GLC002/810 available from Milles Griot Corporation, Irvine, Calif. Lens 806 collimates the generation beam 151, and is mounted on a positioner (not shown) for providing motion to beam 151 with respect to beam 152.

The relation between wavelengths of beams 151 and 152 produced by lasers 801 and 805 is a critical aspect in one embodiment and leads to unexpected results, for example when beam 151 contains photons having energy above silicon's bandgap energy and beam 152 contains photons having energy approximately the same as or less than the bandgap energy. In this example, for a silicon wafer the 830 nm and 1480 nm wavelength beams provide one or more benefits described herein (e.g. generate a negligible percentage of measurement-related carriers).

Profiler 103 also includes an isolator 807, such as part number OIM-12-812 available from Karl-Lambrecht Corp., of Chicago, Ill. Isolator 807 prevents back reflections from entering laser 805. Profiler 103 also includes a photo-diode 821 a that is used to measure the intensity of beam 151 after reflection by wafer 106. Moreover, an anamorphic prism (not shown) is inserted in beam 151 to circularize beam 151 that is generated in a polarized manner by laser 805.

Profiler 103 also includes lenses 808 and 809 that function as 2× beam reducer , with focal lengths of 37.5 mm and 75 mm respectively. Lens 808 mounts on a stage (not shown) to allow adjustment of the position along the X-axis with respect to laser 805, and therefore can be used to de-collimate beam 151, thereby varying the spot size with respect to beam 152. Profiler 103 also includes partially transmissive mirror 810, such as a dichroic mirror that combines beams 151 and 152, thereby to create a combined beam 811. Diodes 821B and 821C are “reference diodes” that are used for absolute calibration of the transmitted and reflected power of a probe beam 152.

Profiler 103 also includes a photo cell 821 b (such as a photo diode) that detects leakage through mirror 810, thereby measuring the forward power of beam 151. Beam 811 passes through 50:50 beam splitter 813, and 90:10 beam splitter 814 to objective lens 815. Objective lens 815 can be, for example, 100×, 0.9 NA lens part number 81814 available from Nikon Corporation of Yokohama, Japan. Lens 815 focuses the combined beam 811 onto the surface of wafer 106.

Profiler 103 also includes photo cell (also called “photo diode”) 821C that is used to measure the forward power in beam 811. Profiler 103 also includes stage 829 that is used to move wafer 106 relative to beam 812 in the X, Y and Z directions. Specifically, stage 829 can be moved in the vertical direction along the Z axis to adjust focus, and in a horizontal plane to adjust the position of region 120 of FIG. 1B relative to beam 812 (also required by step 244 in FIG. 2A).

Beam 812, after reflection by region 120 passes back through objective lens 815 to 90:10 beam splitter 814. Splitter 814 deflects 10% or the return beam to second lens 819 that acts as a microscope eyepiece. Lens 819 has a magnification of, for example, 10×, such as part number 81845 from Nikon of Yokohama, Japan.

After passing through lens 819, the deflected portion of beam 812 is incident on a camera 820, such as model 85400 available from FJW Industries of Palatine, Ill. Lens 819 and camera 820 together form a microscope to allow the measurement of focus, beam size and beam overlay using a vision system, such as model ASP-60CR-11-S available from Cognex Corporation, Boston, Mass.

Ninety percent of the reflected portion of beam 812R passes to beam splitter 813 that diverts the reflected portion through filter 817, such as Schott glass RG830, available from Spindler & Hoyer Corporation of Goettingen, Germany to photo cell 818, such as J16-8SP-RO5M-HS from EG&G Judson of Montgomeryville, Pa., USA.

Filter 817 removes photons of generation beam 151 from combined beam 812R, thereby allowing detector 818 to see only the photons of probe beam 152. Filter 817 is a critical component in one embodiment and provides the unexpected result of eliminating feedthrough of the modulated signal (generated by beam 151) to detector 818 that would otherwise be present when using a prior art system of the type disclosed by Smith as discussed above. In this particular implementation, germanium is used in photo detector 818 to provide sensitivity to photons of wavelength 1480 nanometers that are generated by laser 801.

Profiler 103 includes signal processing circuit 830 and drive circuit 840 that are used respectively to process the reflected portion 812R and to generate the generation beam 151. Specifically, laser driver 842 (such as model 8000 from Newport Corporation of Irvine, Calif.) drives laser 805 to generate beam 151 in response to signal on modulation input terminal 842M. Laser driver 842 includes thermo-electric cooler power supply (not shown) to maintain the stability of laser diodes 805 and 801. Drive circuit 840 also includes reference oscillator 843, such as a bench variable frequency oscillator, that is used to drive a signal on modulation input terminal 842M. Reference oscillator 843 provides 100% modulation of beam 151. Reference oscillator 843 has a frequency that is set manually to a value in the range of 1 Hz to 20,000 Hz to avoid the creation of a wave of carriers in region 130 (FIG. 1C).

Combined beam 812 after reflection by region 120 is incident on photo cell 818 included in signal processing circuit 830. Photo cell 818 converts the power of the instant beam into a current that is supplied to current-to-voltage converter 833 also included in signal processing circuit 830 . Converter 833 can be, for example, a single stage op-amp transimpedance amplifier using an OP-27A integrated circuit available from Burr-Brown of Tuscon, Ariz.

Converter 833 converts the current from photo cell 818 into a voltage that is provided to a single gain stage 834 also included in circuit 830. Gain stage 834 provides an additional signal gain over the gain provided by converter 833, because converter 833 is limited to a few kilohms. The gain in converter 833 is limited because converter 833 is dc coupled, and the power of reflected portion 812R is a few milliwatts, so that excess transimpedance gain will cause converter 833 to saturate.

Converter 833 is ac coupled to amplifier 834. In one embodiment, a constant component of the reflectance (as opposed to the reflectance component at the modulation frequency) is measured from the signal at a node 838 that is located between converter 833 and amplifier 834. Profiler 103 uses the constant component to normalize the intensity measurement, and compares the normalized measurement between wafers (e.g. between a wafer under fabrication and a reference wafer). The voltage signal provided by amplifier 834 is used by a lock-in amplifier 835, such as model 830 available from Stanford Research Systems, Sunnyvale, Calif. Lock-in amplifier 835 is coupled to reference oscillator 843 that provides a signal modulated at the same frequency as the signal on modulation terminal 842 m of laser driver 842. Lock-in amplifier 835 provides a signal indicating the intensity of reflected portion 812R modulated at the frequency provided by oscillator 843 to processor 836, such as a personal computer running software to capture and display the signal in an appropriate manner.

In one implementation, personal computer 836 has a line 837 that is coupled to lines 107 and 108 (described above in reference to FIG. 1A) thereby to control the acts performed by ion implanter 101 and rapid thermal annealer 102 based on measurement of one or more material properties as described herein.

Mobility is a material property that affects current transport in semiconductors 156, and is defined through the following equation: $\begin{matrix} {J = {{q\quad \mu \quad {nE}} - {\frac{kT}{q}\mu \frac{\partial n}{\partial x}}}} & (1) \end{matrix}$

where J is the current density, n is the carrier concentration, E is the electric field, k is Boltzmann's constant, q is the electron charge, T is the temperature, and μ is the mobility. Appearing in both terms of equation (1), mobility μ is the fundamental material constant that defines the current flow (See Sze, “Physics of Semiconductor Devices”, pages 50-51, incorporated by reference herein).

Mobility μ directly relates to fundamental device performance, including speed and power dissipation. For example, in a field effect transistor (the fundamental building block of modern integrated circuits) the transconductance g_(m) (change of current with respect to applied gate voltage) is linearly proportional to the mobility through the factor $\begin{matrix} {g_{m} \propto {\frac{Z}{L}{\mu C}_{0}}} & (2) \end{matrix}$

where Z and L are the channel width and length respectively, and C₀ is the gate capacitance. The mobility near (e.g. within a depth less than the mean free path of the carriers) surface 153 (FIG. 1C) depends on a number of parameters affected by the process, such as surface roughness, doping and defect density (See Grove, “Physics and Technology of Semiconductor Devices”, page 326, incorporated by reference herein).

Lifetime is a measure of how long a carrier exists before it recombines, and is determined from a measurement of the radial decay of the concentration of excess carriers as described herein (e.g. is reference to FIGS. 7A and 7B). Contamination causes the lifetime to drop rapidly, as does an increase in defect density. Thus, lifetime is a sensitive indicator of material quality and process contamination. Near the surface 153 (FIG. 1C), lifetime may be dominated by trapping centers at the interface between a silicon dioxide layer and the silicon. The lifetime near surface 153 becomes an indicator of the quality of this interface.

Active dopants modify the conduction properties of a semiconductor material 156 (FIG. 1C), thereby making devices such as transistors. Active dopants are also used to isolate devices, form contacts, and adjust operating voltage levels. Profiler 103 indicates how much of an implanted dose becomes electrically active and therefore the efficacy of such structures. In many cases, process problems relate to uniformity of the anneal and activation, so that measuring only an implanted dose in an unannealed wafer 105 is of less value than measuring in an annealed wafer 106 a profile of active dopants (e.g. lines 601-604 described above in reference to FIG. 6A).

The photons of beam 151 (FIG. 1C) generate free electron-hole pairs. Because the index of refraction of semiconductor material 156 is large compared to free space (silicon, for example, has a relative index of refraction of 3.42), the incident rays refract sharply to the normal 155, and the beam shape approximates a cylinder 157 for a depth of a few microns (e.g. 5 microns beneath the surface).

When the diffusion length L (the distance excess carriers travel before they recombine, given by L²=(kT/q)μτ, where τ is the lifetime and k is Boltzmann's constant, T the temperature, and q the electron charge) is long compared to the radius w₀ of illuminated region 120—as is commonly the case in some processes—the carrier concentration within this cylinder is independent of radius w₀, and varies as the inverse of the mobility, μ. Furthermore, reflectance relates directly to the carrier concentration C, so that a reflected power measurement provides a direct measure of mobility μ.

Outside the illuminated cylinder, carrier concentration C drops rapidly, the drop being approximately exponential function of the ratio r/L, where r is the radius from the cylinder and L is the diffusion length. Because of the cylindrical geometry, the drop off is a Bessel function, which is the cylindrical symmetry equivalent of an exponential function. Thus, knowledge of the mobility μ from an intensity measurement (see act 243 in FIG. 2A) within illuminated region 120 coupled with another intensity measurement of the carrier concentration as a function of distance from illuminated region 120 allows determination of lifetime τ as described above (in reference to FIGS. 7A and 7B).

Furthermore, in silicon of the type used to make semiconductor devices (such as integrated circuits), the concentration of active dopants directly relates to the mobility. Thus, a measurement of the mobility allows determination of the active dopant concentrations 601Y-604Y (FIG. 6A). Finally, adding a layer of material with a concentration of dopants different from the bulk, as by ion implantation and annealing as described above, affects the reflectance as a function of the power of beam 151 (FIG. 1C), and the function can be used to determine the active dopant profile in the added layer.

Carrier concentrations in a bulk material (i.e. a material that is uniformly doped) can be calculated assuming that the diffusion length L is very long compared to the cylinder radius, i.e. (Dτ>>w₀ ²) so that there is no recombination in the cylinder. In this formula D is the diffusion coefficient D=(kT/q)μ, where μ is the mobility. Thus, the diffusion coefficient and the mobility are directly related. Furthermore, it is assumed that the absorption length α⁻¹ of the beam 151 (FIG. 1C) used to generate carriers is long compared to the cylinder diameter 2w₀, so that the generation is approximately constant in depth d.

Under these assumptions, all carriers generated in cylinder 157 exit out the side, and there is negligible current along the normal 155 that is the axis of the cylinder 157. This case usually applies, since the radius w₀ typically 0.5-3 μm, the diffusion length L may be 20 μm or longer, and the absorption length α⁻¹ is 5-20 μm (the former for a wavelength λ of 670 nanometers, the latter for a λ wavelength of 810 nm).

The rate G of carrier generation per unit volume in a cylinder 157 of radius w₀ (also called “spot size”) in a region between depth z and z+dz is

G(r)=πr ²(1−R)Φ(e ^(−αz) −e ^(−α(z+dz)))≈πr ²(1−R)Φαe ^(−αz) dz,  (3)

where r is the distance from normal 155, R is the surface reflectance, F is the incident photon flux of beam 151, w₀ is the radius of cylinder 157, and α is the absorption coefficient of material 156.

The flux F out of a cylinder of radius r is this number G of carriers generated per unit time per unit volume found in equation (3), divided by the area of the wall of cylinder 157, $\begin{matrix} {{F(r)} = {\frac{G}{2\pi \quad {rdz}} = {\frac{\alpha \quad {r\left( {1 - R} \right)}\Phi \quad e^{- {az}}}{2} = {{{- D}\frac{\partial n}{\partial r}} = {{- \frac{kT}{q}}\mu {\frac{\partial n_{e}}{\partial r}.}}}}}} & (4) \end{matrix}$

The last two equalities in equation (4) are due to the fact that the flux F is limited to diffusion (in the absence of a wave), and a relationship between the diffusion coefficient D and mobility μ is applied from an equation (6) to be discussed below.

This solution in equation (4) ignores surface recombination of charge carriers. One embodiment of the invention is used on semiconductor wafers undergoing integrated circuit processing, and these wafers usually have surface passivation, that suppresses surface recombination.

The carrier concentration in a cylinder is independent of the cylinder's radius under the conditions described herein as shown below. Integrating both sides of equation (4) with respect to r from zero to the cylinder radius gives $\begin{matrix} {{n_{e}\left( w_{0} \right)} = {{\int_{0}^{w_{0}}{\frac{\partial n}{\partial r}\quad {r}}} = {{\frac{{q\left( {1 - R} \right)}\alpha \quad e^{- {az}}}{4\pi \quad {kT}\quad \mu}\left( {\pi \quad w_{0}^{2}\Phi} \right)} = {\left\lbrack \frac{{q\left( {1 - R} \right)}\alpha \quad e^{- {az}}}{4\pi \quad {kTE}_{p}} \right\rbrack \left( \frac{1}{\mu} \right)P_{1}}}}} & (5) \end{matrix}$

where P_(l) is the power of generation beam 151, E_(p) is the energy of a single photon, and the mobility and diffusivity relate as $\begin{matrix} {D = {\frac{kT}{q}\mu}} & (6) \end{matrix}$

where k, T and q have been described above in reference to diffusion length L. Equation (5) shows that when the spot size (also called “beam diameter”) w₀ is small, excess carrier concentration n_(e) in any cylinder is independent of radius, and is solely a function of known physical parameters (a constant shown in square brackets in equation (5)), and the inverse of mobility μ.

Therefore, a measurement of intensity of probe beam 152 after reflection by the charge carriers anywhere in illuminated region 120 (FIG. 1C) on surface 153 of semiconductor material 156 provides a direct measure of mobility μ (scaled by the just-described constant) when power Pl of the generation beam 151 is 1 watt.

In one embodiment, the reflected intensity of beam 152 as a function of power of beam 151 is measured. As shown below, the reflected intensity varies linearly with carrier concentration n_(e). Therefore, a plot of reflected intensity v/s generation beam power for a wafer without a doped layer at the surface, as shown by line 901 in FIG. 9A, approximates a straight line. The slope of line 801 is the product of known physical parameters and the inverse of the mobility.

Therefore, equation (5) illustrates the physical basis of the measurement of carrier concentration n_(e) by profiler 103 within the illuminated region. The exact solution for the carrier concentration n_(e) is found using the diffusion equation in cylindrical coordinates, $\begin{matrix} {\frac{\partial n_{e}}{\partial t} = {G - \frac{n_{e}}{\tau_{0}} + {D\left( {\frac{\partial^{2}n_{e}}{\partial r^{2}} + {\frac{1}{r}\frac{\partial n_{e}}{\partial r}}} \right)}}} & (7) \end{matrix}$

where n_(e) is the concentration of excess carriers and G is the generation rate per unit volume, with

G=αΦ  (8)

where, as above, Φ is the incident photon flux per unit area and α is the absorption coefficient.

For periodically varying incident radiation, all quantities vary in time as exp(jωt), and (7) reduces to $\begin{matrix} {{\left( {\frac{\partial^{2}n_{e}}{\partial r^{2}} + {\frac{1}{r}\frac{\partial n_{e}}{\partial r}}} \right) - {n_{e}\left( {\frac{1}{D\quad \tau_{0}} + {j\frac{\omega}{D}}} \right)} + G} = 0} & (9) \end{matrix}$

To avoid creation of a wave of charge carriers as described herein, the real part of the second term in equation (9) needs to be significantly larger than the imaginary part, a condition that requires the frequency ω=2πf=1/10τ₀. For a lifetime of 10 μsec, the modulation frequency f should be less than 1600 Hz. The imaginary part of equation (9) when significantly larger than the real part leads to a wave-like solution at high frequencies and is avoided under the conditions described herein. The present invention operates at sufficiently low frequencies, to allow the imaginary term to be dropped. This assumption reduces equation (9) to

ρ² n″(ρ)+ρn′(ρ)−ρ² n(ρ)=0  (10)

where r²=r²/Dt₀=r²/L² and n=n_(e)−G t₀.

The solution to equation (10) is written in terms of the hyperbolic Bessel functions of order zero, $\begin{matrix} {{n\left( \frac{r}{L} \right)} = {{{AI}_{0}\left( \frac{r}{L} \right)} + {{BK}_{0}\left( \frac{r}{L} \right)}}} & (11) \end{matrix}$

where K₀ tends to zero at infinity and becomes infinite at zero. Conversely, I₀ diverges as r approaches infinity but tends to zero for small arguments. Consequently, within the cylinder 157 formed by beam 151 (FIG. 1C), A is finite and B is zero. Outside the cylinder, B is finite and A is zero. The coefficients A and B are found by recognizing that the carrier concentration C and its derivative are continuous at the cylinder wall, r=w₀.

Applying the above conditions gives the exact solutions as follows, where “n” is the carrier concentration that is in excess of the concentration with zero illumination: $\begin{matrix} {{{n\left( {r \leq w_{0}} \right)} = {G\quad {\tau \left\lbrack {1 + \frac{{K_{1}\left( \frac{w_{0}}{L} \right)}{I_{0}\left( \frac{r}{L} \right)}}{{{K_{0}\left( \frac{w_{0}}{L} \right)}{I_{1}\left( \frac{w_{0}}{L} \right)}} - {{I_{0}\left( \frac{w_{0}}{L} \right)}{K_{1}\left( \frac{w_{0}}{L} \right)}}}} \right\rbrack}}}\quad {and}} & \text{(12a)} \\ {{{n\left( {r \geq w_{0}} \right)} = {G\quad \tau \frac{{I_{1}\left( \frac{w_{0}}{L} \right)}{K_{0}\left( \frac{r}{L} \right)}}{{{K_{0}\left( \frac{w_{0}}{L} \right)}{I_{1}\left( \frac{w_{0}}{L} \right)}} - {{I_{0}\left( \frac{w_{0}}{L} \right)}{K_{1}\left( \frac{w_{0}}{L} \right)}}}}}\quad} & \text{(12b)} \end{matrix}$

FIG. 9A shows lines 901-904 that illustrate the solution inside equation (12a) and outside equation (12b) illuminated region 120. Equation (12a) yields the same result as equation (5) for w₀<<L. Specifically, FIG. 9A illustrates, in a graph, curved lines 901-904 that indicate the logarithm (along the y axis)of carrier concentration (for corresponding doping concentrations) as a function of the radial distance (along the x axis) from the central axis 155 (FIG. 1C), with no ion implants in the respective wafers. The doping concentrations for curved lines 901-904 are respectively 10¹⁹, 10¹⁸, 10¹⁷, and 10¹⁶ atoms/cm³, and the measurements were taken about r=0, where beams 151 and 152 (FIG. 1C) overlay. As beam 151 is cylindrically symmetric, the linear coordinates (different from angular coordinates θ) are depth D and radius r.

In FIG. 9A, the carrier concentration (vertical axis) is shown as a function of radius near surface 153 (depth=0) resulting from illumination by an generation beam 151 (FIG. 1C) of uniform spatial intensity (e.g. assume a constant beam intensity for a radius between zero (the beam axis) and the beam radius w₀ (FIG. 1C), and zero intensity beyond the beam radius w₀). The beam radius w₀ in one example is 0.5 μm the power is 20 milliwatts, and the wavelength is 810 nanometers (for silicon).

As shown herein, the carrier concentration n_(e) in region 120 (FIG. 1C) is constant, independent of beam radius w₀, and inversely proportional to the mobility of the charge carriers. The mobility is inversely proportional to the doping concentration, so the carrier concentration increases with doping. Also, the reflectance measurement increases linearly with the carrier concentration, and so the reflectance measurement provides a measure of 1/mobility.

The rate at which the concentration n_(e) drops outside illuminated region 120 (FIG. 1C) is a function of the lifetime τ and the diffusion length L=(Dτ)^(½). Since D is known from the reflectance measurement within illuminated region 120, a set of reflectance measurements radially outward from the cylinder edge determines the lifetime τ.

Carrier concentration n_(e) can also be determined in material with a shallow doped layer 911 (FIG. 9B) formed by introduction of dopant atoms through surface 153. FIG. 9C illustrates a semiconductor structure in wafer 105/106 under illumination, the potential drop across the structure, and the currents out of the region of the shallow doped layer under illumination. Regions 912-914 are, respectively, a shallow doped layer, a low doped epitaxial layer, and a high doped substrate. All are assumed to be doped p-type, although n-type doping, or various combinations of n- and p-type doping give similar results. Junction 916 exists between shallow doped layer 912 and epitaxial layer 913.

The semiconductor surface 923 is illuminated with laser beam 911, creating a cylindrical region of illumination in the substrate, and illuminating region 915 of shallow doped layer 912. The illumination causes a potential drop across the structure, with the surface at the most negative point. Most of the potential drop is taken up at the interface between the epitaxial layer 913 and substrate 914, drop 918, and the interface between the shallow doped layer 912 and epitaxial layer 913, drop 919. Lesser drops occur in the substrate 914, epi layer 913, and shallow doped layer 912, which are drops 920, 921 and 922 respectively.

Two currents flow out of the shallow doped layer 913. One is a vertical current 917, flowing perpendicular to the surface. The second is a radial current 916, flowing parallel to the surface. These currents are assumed to be due to diffusion. There are four components: the vertical hole current, the vertical electron current, the radial hole current, and the radial electron current. These are, respectively: $\begin{matrix} {J_{Vp} = {{- {qD}_{p}}\frac{p}{z}}} & \text{(13a)} \\ {J_{Vn} = {{qD}_{n}\frac{n}{z}}} & \text{(13b)} \\ {J_{Rp} = {{- {qD}_{p}}\frac{p}{r}}} & \text{(13c)} \\ {J_{Rn} = {{qD}_{n}\frac{n}{r}}} & \text{(13d)} \end{matrix}$

where q is the electron charge, D_(p) and D_(n) are the hole and electron diffusion coefficients respectively, p is the hole concentration, n is the electron concentration, z is the variable in the depth direction, and r is the variable in the radial direction. D_(p) and D_(n) are related to the electron and hole mobilities as D_(n(p))=(kT/q)μ_(n(p)), where k is Boltzmann's constant, T is the temperature, and μ_(n(p)) is the electron (hole) mobility.

A qualitative analysis (described below) of the structure shown in FIG. 9C explains how the surface carrier concentration, and, hence, the reflection signal, is a function of the power of generation beam 911. The qualitative analysis further explains how the curve may have inflection points and regions with differing slopes, as shown by line 471 in FIG. 4B (described above), and how material properties related to a profile of dopants in the shallow doped region 912 are extracted from curve 471.

Currents 916 and 917 are driven by the gradient of the carrier concentration, as shown in equations 13a-d above. The gradient in the vertical direction scales as the carrier concentration divided by the junction depth. The gradient in the radial direction scales as the carrier concentration divided by the diffusion length in layer 912. Typically, the junction depth is 0.02-0.1 μm and the diffusion length is several microns, so at low level injection the vertical current dominates.

The carrier concentration at the surface is found by integrating current 917, given by equations 13a and 13b, from the surface 923 to the junction 916, with the boundary condition that the carrier concentration must be zero at junction 916 since, according to potential drop 919, junction 916 is reverse biased. This integral increases with junction depth. Therefore, the signal at low level injection is sensitive to junction depth. Experimental results, such as line 511 in FIG. 5D (described above), confirm this dependence.

Under high level injection, the effect of the background doping concentration disappears, and the potential drop 919 across the junction between regions 912 and 913 disappears. The gradient of the carrier concentration in the vertical direction is now due to the optical absorption of photons, a distance characterized by the absorption length. The gradient of the carrier concentration in the radial direction is still due to the diffusion length in layer 912.

For 830 nm radiation, the absorption length is about 20 μm. The radial gradient is on a scale of 2-4 μm (see, for example, the decay of the radial electron concentration lines 701 and 702 in FIG. 7A). Now, the radial current 916 is larger than the vertical current 917. The surface carrier concentration is sensitive to the near-surface mobility, and sensitivity to the junction depth disappears.

According to the above description, line 471 (FIG. 4B) when fit in the region below inflection point IP (FIG. 4B), corresponds to low level injection, as illustrated by straight line 471L, and to the region above inflection point 471I, by straight line 471H. The slope and intercept of line 471L are each used to characterize the junction depth and the slope and intercept of line 471H are each used to characterize the mobility near the surface. As the inflection point IP occurs at the transition from low to high level injection (as described above in reference to FIG. 4B), at this point the excess carriers have a concentration that approximately equals the doping concentration. Thus, shifts in the inflection point IP correspond to shifts in the doping concentration.

Because of the complexity of the equations governing a doped layer in the real world (as compared to the just-described model illustrated by regions 912-914 in FIG. 9A), the concentration of excess carriers n_(e) is obtained by using numerical modeling by computer 103C, rather than analytical equations. Such solutions, as well as actual measurements (see for example, FIG. 5B) have various attributes such as inflection points that are used to determine the various material properties (such as surface concentration, mobility and junction depth) as described above.

Lines 951-953 (FIG. 9B) illustrate surface carrier concentration C in illuminated region 120 as a function of power of generation beam 151, as obtained from numerical modeling. Specifically, lines 951-953 are for doping concentrations of 10¹⁶, 10¹⁷, and 10¹⁸ atoms/cm³, for a 0.2 μm thick implanted layer, on an epitaxial layer doped p-type at a level of 10¹⁶ atoms/cm³, with beam 151 having radius 0.5 μm and wavelength 810 nm for structure 910.

For line 951, regions 912 and 913 have the same doping concentration, and the carrier concentration (at surface 923) as a function of power of generation beam 151 is a straight line, with the slope determined by the mobility. Inflection points 912I and 913I move to higher levels of power of generation beam 151 with increasing doping concentration, and the slopes m_(H) at high level injection (slopes of regions 912H and 913H) drop as the doping increases, reducing the mobility. The slopes of line 951 and region 952H are approximately equal because the mobility drops only slightly (e.g. less than 5%) between 10¹⁶ and 10¹⁷/cm³ doping.

As with bulk material 912 discussed above, the mobility and lifetime of layer 911 may also be found. To account for the complexity introduced by the multi-layered structure 910, a numerical model is created by computer 103C, and then fit with data such as carrier concentration C vs. laser power p and vs. radius r from the optical axis 155 (FIG. 1C) to determine material properties e.g. the mobility and lifetime. For example, the numerical model may indicate that an intensity measurement of a certain value (also called “expected value”) is expected from a certain doped layer. If the mobility near the surface is degraded, the measured value is altered from the expected value, thus identifying a problem.

A reflected signal that is measured in step 243 (FIG. 2A) arises from the change in the surface reflection coefficient (also called “reflectance”) due to concentration of excess carriers caused by beam 151 (FIG. 1C). The excess carriers (not shown) oscillate in the electric field of beam 151 illuminating the surface 153 (FIG. 1C). The oscillating carriers re-radiate light from beam 152. This re-radiated light adds to the reflection of beam 152 that occurs normally even in the absence of the excess carriers.

A solution for the reflected signal can be found analytically as described below using the Drude theory of conduction (see Handbook of Optics, Volume II, pages 35.3-35.7; Jackson “Classical Electrodynamics”, sec. 7.7 and 7.8). The propagation constant in gaussian units for a poor conductor (4ps/we<<1) is $\begin{matrix} {k = {{m\left( \frac{\omega}{c} \right)} = {\left\lbrack {\sqrt{\mu_{m}ɛ}\left( {1 + {i\quad \frac{2\quad \pi \quad \sigma}{ɛ\quad \omega}}} \right)} \right\rbrack \left( \frac{\omega}{c} \right)}}} & (14) \end{matrix}$

where s is the conductivity, ω is the radial frequency of the light, c is the speed of light, m is the index of refraction, μ_(m) is the magnetic permeability, and ε is the dielectric permittivity The first term is the complex index of refraction. In the present case, the magnetic permeability μ_(m)=1, and ε=m₀ ², where m₀ is the index of refraction in the absence of illumination (3.42 for silicon).

From the Drude theory, the conductivity in the infrared is $\begin{matrix} {\sigma = {{{- \frac{{n_{e}(r)}q^{2}}{{im}_{e}^{*}\omega}} - \frac{{n_{h}(r)}q^{2}}{{im}_{h}^{*}\omega}} = {{- \frac{q^{2}}{i\quad \omega}}\left( {\frac{n_{e}(r)}{m_{e}^{*}} + \frac{n_{h}(r)}{m_{h}^{*}}} \right)}}} & (15) \end{matrix}$

where q is the electron charge, m_(e)* and m_(h)* are the electron and hole effective masses, and n_(e) and n_(h) are the electron and hole concentrations.

For silicon, the hole effective mass is independent of orientation. The electron effective mass, however, is orientation dependent, varying from 0.19 to 0.98 times the electron mass. For light illuminating a (100) crystal surface—this cut being the most common in integrated circuit processing—the effective mass has four-fold symmetry. Consequently, a reflected signal due to illumination with a polarization vector that rotates at a frequency f has a 4f frequency component due to the electrons, provides a means for measuring the electron concentration.

The imaginary conductivity means that the propagation constant in equation (14) is real. This is because optical frequency is so high that the electric field moves the carriers a very small distance and they do not collide with the lattice. The result is that they do not give up energy, so there is no absorption.

Combining equations (14) and (15), and multiplying the conductivity by ¼pe₀ to convert to MKS units, the index of refraction is $\begin{matrix} {m = {{m_{o} + {\Delta \quad m}} = {\sqrt{ɛ} - {\frac{q^{2}}{2ɛ_{o}m_{o}m^{*}\omega^{2}}\left( {\frac{n_{e}(r)}{m_{e}^{*}} + \frac{n_{h}(r)}{m_{h}^{*}}} \right)}}}} & (16) \end{matrix}$

For normal incidence on conductive media from air (index of refraction=1), the reflection coefficient is given by $\begin{matrix} {R = \frac{\left( {1 - \eta} \right)^{2} + \kappa^{2}}{\left( {1 + \eta} \right)^{2} + \kappa^{2}}} & (17) \end{matrix}$

This equation is an approximation, because probe beam 152 is focused on the surface 153 (FIG. 1C), so that the incident rays are not normal. However, the approximation is suitable to estimate the performance of profiler 103, and simplifies the analysis.

The variables in equation (17) relate to the index of refraction m by

m=η+iκ  (18)

and the imaginary (absorption) term is related to the absorption coefficient of the medium by $\begin{matrix} {\kappa = \frac{\alpha \quad \lambda}{4\quad \pi}} & (19) \end{matrix}$

The form of the change in reflectance ΔR due to a change in index Δm is found as follows. Ignoring the component of reflectivity due to absorption, which is typically very small, the reflectivity is $\begin{matrix} {R = {{\frac{\left( {m - 1} \right)^{2}}{\left( {m + 1} \right)^{2}} \approx {\frac{\left( {m_{0} - 1} \right)^{2}}{\left( {m_{0} + 1} \right)^{2}}\left( {1 + \frac{4\quad \Delta \quad m}{m_{0}^{2} - 1}} \right)}} = {R_{0}\left( {1 + \frac{4\quad \Delta \quad m}{m_{0}^{2} - 1}} \right)}}} & (20) \end{matrix}$

where the approximation is found by substituting an index of refraction of the form m=m₀+Δm, and retaining terms to order Δm. From equation 20, $\begin{matrix} {{\Delta \quad {R\left( r_{r} \right)}} = {\frac{4\quad \Delta \quad {m\left( r_{r} \right)}}{m_{0}^{2} - 1}R_{0}}} & (21) \end{matrix}$

The form of the change in index is found from the Drude theory (equation 20 above), $\begin{matrix} {{\Delta \quad {m\left( r_{r} \right)}} = \frac{q^{2}{n\left( r_{r} \right)}}{2\quad \varepsilon_{0}\varepsilon_{s}m^{*}\omega^{2}}} & (22) \end{matrix}$

where q=1.602×10⁻¹⁹ coulomb is the electron charge, ε₀=8.86×10⁻¹² F/m is the dielectric constant of free space, ε_(s)=11.7 is the relative dielectric constant of silicon, m* is the carrier effective mass, and w is the radial frequency of the infrared beam, ω=2pc/l, where c=3×10⁸ m/sec is the speed of light and 1 is the wavelength. In equation (22), n(r_(r)) is the radial carrier distribution, given by equation (12a) within the region 120 illuminated by generation beam 151, and equation (12b) outside the illuminated region 121, or as found using numerical models.

Therefore, in one embodiment, computer 103C (FIG. 1A is programmed to use equations (21) and (22) to determine the carrier distribution n(r_(r)). Note that computer 103C multiplies n(r_(r)) by 10⁶ to convert from /cm³ to /m³ if the constants given above are used, and the effective mass is in kilograms.

In equation (22) the electron and hole concentrations are assumed to be equal, since a photon generates an electron-hole pair, and net charge neutrality generally exists. For convenience, the electron and hole effective masses are considered equal, although this will not always be true.

Therefore, carrier concentration C is measured by profiler 103 (FIG. 1A) overlaying two beams (as shown in FIG. 1C): (1) generation beam 151 that generates excess carriers, and (2) probe beam 152 used to measure the reflectance attributable to the excess carriers. Wavelength l of the generation beam 151 is, in one embodiment, shorter than the wavelength of the probe beam 152, since the photon energy varies inversely with the wavelength, according to the relation $\begin{matrix} {E_{ph} = {h\frac{c}{\lambda}}} & (23) \end{matrix}$

where h is Plank's constant and c is the speed of light.

Furthermore, the minimum spot size w₀ varies with the wavelength as $\begin{matrix} {w_{o} = \frac{0.61\quad \lambda}{NA}} & (24) \end{matrix}$

where NA is the numerical aperture of the focusing lens 415 (FIG. 8A).

As these relations indicate, probe beam 152 has a larger minimum spot size than generation beam 151 when both beams 151 and 152 use identical lenses and have identical diameters. However, as discussed above, relative beam diameters can be chosen to make beams 151 and 152 of equal diameter at surface 153 (FIG. 1I). In one embodiment, equation (24) is used by computer 103C to measure the lifetime of the semiconductor material 156 (FIG. 1C), since the carrier concentration C decays away from the region illuminated by generation beam 151 as a function of $\sqrt{D\quad \tau},$

where τ is the lifetime.

In a first approach, profiler 103 overlays the axes of both beams 151 and 152 and starts with probe beam 152 larger than generation beam 151. Then, profiler 103 gradually expands the size of generation beam 151 until beam 151 is as large as probe beam 152. During the process, profiler 103 measures the reflectance at each of a number of sizes of the generation beam 151, and plots these measurements to obtain a curved line, followed by determining various attributes (e.g. coefficients) for the curved line. Therefore, profiler 103 compares the coefficient values for a region (e.g. through a graph) with coefficient values of regions having known material properties, thereby to interpolate one or more material properties of the region.

In a second approach, profiler 103 overlays the two beams 151 and 152 with both at their minimum size. Then profiler 103 scans the generation beam 151 back and forth along a line, with the scan amplitude approximately equal to the diameter of probe beam 152. During the scanning, profiler 103 measures the reflected intensity, and provides an AC (alternating current) signal. Such an AC signal is detected with improved signal-to-noise ratio as compared to a direct current (DC) signal.

FIG. 1G shows the geometry of scanning one beam with respect to the other to determine a profile of the concentration of excess carriers as a function of distance along surface 153. The radii of the probe and generation beams 152 and 151 are Wp and Wg respectively. The axis of generation beam 151 is displaced from the axis of probe beam 152 by a distance Dx along the x axis, wherein the x and y axes define the surface plane of a wafer 105/106.

The power of a reflected portion of probe beam 152 is found by integrating the reflection coefficient over the area of the probe beam 152. A point within the probe beam 152 defined in cylindrical coordinates as (r, φ) is a distance $\begin{matrix} {r_{r} = {{r\sqrt{\left( {{\cos (\varphi)} - \frac{\Delta \quad x}{r}} \right)^{2} + {\sin (\varphi)}^{2}}} = {r\sqrt{1 - {2\frac{\Delta \quad x}{r}{\cos (\varphi)}} + \left( \frac{\Delta \quad x}{r} \right)^{2}}}}} & (25) \end{matrix}$

from the origin of generation beam 151. The reflected power is then given by $\begin{matrix} {P_{ref} = {\int_{0}^{{2\quad \pi}\quad}{\int_{0}^{w_{IR}}{{I_{i}(r)}\Delta \quad {R\left( r_{r} \right)}r\quad {r}\quad {\varphi}}}}} & (26) \end{matrix}$

where I_(i)(r) is the incident intensity of probe beam 152. For a uniform beam, I_(i)(r)=P_(IR)/(pw_(ir) ²), and $\begin{matrix} {P_{ref} = {\frac{P_{IR}}{\pi \quad w_{IR}^{2}}{\int_{0}^{{2\quad \pi}\quad}{\int_{0}^{w_{IR}}{\Delta \quad {R\left( r_{r} \right)}r\quad {r}\quad {\varphi}}}}}} & (27) \end{matrix}$

A method of measuring material properties using equation (27) is described above in reference to FIG. 7B. For example, FIG. 7B shows the excess carrier concentration (y axis) as a function of radial position displaced from the axis 155 of generation beam 151. As probe beam 152 is displaced according to the above procedure, probe beam 152 illuminates a region having a smaller number of carriers, and the reflection signal drops. The magnitude of this drop, and of the peak signal, is a function of the lifetime. A greater signal is obtained from a wafer without degraded lifetime (line 711) as opposed to a wafer with degraded lifetime (line 712).

Signal-to-noise ratio (SNR) can also be determined for the measurement method (e.g. method 200) described herein. The reflected signal is given by using equation (20) for the real part of the index, equation (23) for the imaginary part, and equation (21) for the fraction of power reflected,

ΔP=(R−R ₀)P _(lw)  (28)

where $\begin{matrix} {R_{o} = \frac{\left( {1 - m_{o}} \right)^{2}}{\left( {1 + m_{o}} \right)^{2}}} & (29) \end{matrix}$

and P_(lw) is the laser power of probe beam 152 at the wafer surface 153 (FIG. 1C).

The noise of the system is dominated by the shot noise in the detector photocell 818. The RMS shot noise power in the photocell 818 is $\begin{matrix} {P_{noise} = \sqrt{\frac{2{qR}_{o}P_{1w}{L({BW})}}{A}}} & (30) \end{matrix}$

where BW is the bandwidth, A is the conversion efficiency of the photocell, and L is the loss in transmission through the optical system. For a reflectance R₀=0.35, laser power P_(lw)=100 mW, a loss L=0.2, a lock-in amplifier noise bandwidth of 0.3 Hz, and a conversion efficiency of A=0.6 amps/watt, the noise power is P_(noise)=34 picowatts. For a typical reflectance signal ΔR/R=10⁻⁶, where ΔR is the change in reflectance due to the concentration of excess carriers at the surface, the signal power is 20 nanowatts, and the signal-to-noise ratio (SNR) is 588. This is well above the SNR of 100 required to obtain a ±1% accuracy.

Although the generation beam 151 is modulated, the probe beam 152 is operated continuously at constant power (without modulation). The just-described act of beams 151 and 152 allows separation in measurement of two reflectances: a reflectance caused by the excess carriers from the background reflectance, since the former changes at the modulation frequency and can be detected in a synchronous manner.

The above calculations did not include the heating of surface 153 due to absorption of energy from generation beam 151. Such heating has the effect of reducing mobility. The temperature of region 120 (FIG. 1C) can be calculated using the radial diffusion equation. For silicon, limiting the incident power of generation beam 151 to a power on the order of 100 milliwatts limits the heating to a few (e.g. less than 10) degrees Centigrade, and therefore the above calculations still hold.

Alternatively, by increasing the power of generation beam 151, profiler 103 measures mobility as a function of temperature, thereby measuring mobility at the temperature that an integrated circuit in wafer 105/106 is expected to operate.

As described above, beam 151 that is used to generate carriers has photons of energy (also called “photon energy”) greater than the bandgap energy of the semiconductor material, and beam 152 that is used to measure reflection has a photon energy lower than the bandgap energy. Therefore, the bandgap energy defines a “boundary line” between the photon energies of two beams 151 and 152 used in one embodiment. The use of two beams, one on each side of such a boundary line is a critical aspect in this embodiment. At 300 degrees Kelvin, the boundary line is 1.12 eV (wavelength of 1.11 μm) for silicon, 1.42 eV (0.87 μm) for GaAs, 0.66 eV (1.88 μm) for Ge, and 1.35 eV (0.92 μm) for InP.

In an alternative method, an act 1800 (FIG. 11) uses a polarized beam (not shown) of light that is focused (act 1801) onto surface 163 (FIG. 10A) of a semiconductor material 166 that has charge carriers generated (act 1802) by focusing an generation beam 151 (FIG. 1C) modulated as described above. The polarized beam is reflected (act 1803 in FIG. 11), and undergoes a polarization rotation upon reflection. The polarization rotation is caused by different reflection coefficients for the polarization components parallel and perpendicular to surface 163. The rotation is a function of the index of refraction. Therefore profiler 103 interferes (act 1804) the reflected portion with an unreflected portion of the incident beam, and measures (act 1805) a difference in magnitudes between the sum and difference components at the modulation frequency.

Thereafter, profiler 103 relates (act 1806) the measured difference to a property of the semiconductor material. Act 1806 is similar to act 250 described above in reference to FIG. 2A. However, in act 1800, instead of acts 244 and 241, profiler 103 performs the respective acts 1807 and 1808 and uses the measured differences to determine the material property in act 1806 as described herein.

The index of refraction is changed as a result of a change in the carrier concentration, as described by equation 22. A beam of polarized light reflected from surface 163 undergoes rotation of polarization that is a function of the index of refraction at surface 163. A measurement of this rotation is used to measure the change of index of refraction and, using equation 22, the concentration of excess carriers at surface 163.

Specifically, the polarization rotation measurement is used to measure material properties in a manner identical to the use of reflectance measurements as described earlier, in reference to FIGS. 5A-5H. Therefore, act 1800 (FIG. 11) is performed by profiler 103 (FIG. 1A) instead of act 240. That is, profiler 103 performs one or more of acts 210, 211, 213, 220 and 230 prior to act 1800, and performs acts 250 and 260 subsequent to act 1800, while using the polarization rotation measurement instead of the intensity measurement.

Moreover, profiler 103 measures various material properties of the semiconductor material (such as the dopant concentration, mobility, junction depth, lifetime, and defects that cause leakage of current during the act of an FET) in the manner described above except that profiler 103 uses the polarization rotation measurement instead of the intensity measurement. For example, in an act similar to the above-described act 243 (FIG. 2A), a number of polarization rotation measurements are obtained in a single location by changing the power of generation beam 151, and the measurements are plotted against the corresponding powers in a graph similar to FIG. 5A. Thereafter the slope of a line connecting the measurements is obtained and inverse of the slope indicates mobility as described above.

Specifically, a scaling factor is determined based on measurement of a reference sample, (similar to intensity measurement conversion to mobility as described above), to convert from units of signal to units of doping. The rotation measurements can also be performed in an offset position (FIG. 1F),or with generation and probe beams of differing size (FIG. 1G) to yield lifetime. Moreover, coincident beams 151 and 152 (FIG. 1C) can be scanned across a wafer in a manner similar to that described above in reference to FIGS. 3A and 3B, to identify changes in the material properties of the wafer.

At non-normal incidence of a light ray in the probe beam (not shown), there are two different reflection coefficients: One for the component of the electric field in the plane of the surface (called the “s component”) and one for the component in a plane perpendicular to the plane of the surface (called the “p component”). The reflection coefficients for the s and p components are both functions of angle and the index of refraction of the semiconductor material 166 (FIG. 10), but have different forms. Consequently, the ratio of the s and p components is different before and after reflection. The reflected light emerging from a lens 168 has a different polarization from the incident light.

This polarization rotation is measured by interfering the reflected light with a reference beam coherent with the incident beam. Such a measurement may provide an increase in sensitivity of about two orders of magnitude over the use of a non-polarized beam (in act 240 of FIG. 2A), as described below in reference to equation (48).

A plane wave with polarization along the x axis illuminates a lens 168 (FIG. 10A). The incident plane wave has an electric field amplitude E_(ix). The plane wave illuminating lens 168 is made up of a set of rays of light. To derive the polarization rotation, the following analysis traces one of these rays as it reflects from interface 163.

Specifically, a ray Ri of the polarized beam intercepts lens 168 at a radius r and angle φ with respect to the x axis. Lens 168 diffracts ray Ri so that diffracted ray R_(d) propagates toward the focus f, located at the origin, a distance f from lens 168 along the z axis. Diffracted ray Rd has electric field components E_(is), parallel to the x-y plane (a plane parallel to the wafer surface), and E_(ip) in a plane perpendicular to the x-y plane. The angle of the diffracted ray Rd with respect to the z axis is q.

After reflection, ray Rr has electric field components E_(rs)=r_(s)E_(is) is and E_(rp)=r_(p)E_(ip), where r_(s) and r_(p) are the amplitude reflection components. These components are illustrated as a function of angle in the graph in FIG. 10B. Since r_(s) and r_(p) are equal only at q=0 (for a ray along the z axis), the ratios E_(ix)/E_(iy) and E_(rx)/E_(ry) are not equal, and the polarization of reflected ray RR is rotated with respect to incident ray RI (the polarization is the direction of the electric field vector, which is the vector sum of the s- and p-components, as shown in the graph in FIG. 10C.

Reflected ray r_(r) (FIG. 10A) strikes lens 168 at a radius r. The lens refracts the reflected ray parallel to the z axis. Refracted ray rr emerges parallel to the incident ray, but with a changed polarization.

The reflection coefficients r_(s) and r_(p) are functions of the angle of incidence and the index of refraction. A change in the index of refraction causes a shift in both reflection coefficients, as shown qualitatively by the dotted lines in the graph in FIG. 10B. Consequently, any change in the index of refraction causes a change in the polarization of the exiting ray RP. An interferometer measures the polarization rotation resulting from any change in the index of refraction of the silicon.

A profiler 1900 (FIG. 12) that uses polarization as described above includes elements 1918, 1930, 1931, and 1932 a and b that together form an interferometer. Profiler 1900 operates in a manner similar or identical to the above-described act of profiler 103 except for the following differences.

50:50 beam splitter 1913 diverts 50% of the reflected beam to the left, in the direction of the detectors. Splitter 1913 also diverts 50% of the beam incident from lasers 1901 and 1905 to the right to create the reference beam. Phase plate 1930 is a retarder that is rotated to align the polarization of the reference beam. Mirror 1931 reflects the reference beam back toward the detector. The net retardation of the reference beam is double the retardation from a single pass through phase plate 1930. Both the reference beam and the reflected beam pass through narrow band filter 1917 to remove the generation beam radiation from laser 1905, allowing only radiation at the probe beam wavelength from laser 1901 to reach the detector.

Polarizing beam splitter 1918 interferes the two beams. Splitter 1918 is aligned with polarization axes at approximately 45° to polarization axes of the reflected and reference beams, so that components representing the sum and difference of the reflected and reference beam electric fields are sent to detectors 1932 a and 1932 b. The currents from detectors 1932 a and 1932 b, which are germanium photodiodes, are converted to voltages using trans-impedance amplifiers. The voltages from the two amplifiers are subtracted from one another to provide a signal that is fed to the lock-in amplifier and detected with reference to the modulation of the pump laser 1905.

Assume an incident electric field polarized along the x-axis with amplitude $\begin{matrix} {E_{0} = \sqrt{\frac{P_{1}}{\pi \quad w^{2}}}} & (34) \end{matrix}$

where P_(l) is the probe laser power incident at the objective lens and w is the beam radius. Through ray tracing, the reflected beam vector emerging from lens 168 (FIG. 10A) is $\begin{matrix} \begin{matrix} {E_{r} = {E_{0}\left( {\frac{E_{rx}}{E_{0}},\frac{E_{ry}}{E_{0}}} \right)}} \\ {= {{E_{0}\left( {{{r_{p}{\cos^{2}(\varphi)}{\cos (\theta)}} - {r_{s}{\sin^{2}(\varphi)}}},{{\sin (\varphi)}{\cos (\varphi)}}} \right)}\left( {{r_{p}{\cos (\theta)}} + r_{s}} \right)}} \end{matrix} & (35) \end{matrix}$

where r_(s) and r_(p) are the amplitude reflection coefficients for the s- and p-polarizations, and transmission loss in the lens has been ignored. The amplitude reflection coefficients are given by the relations $r_{s} = {- \frac{\sin \left( {\theta - \theta_{1}} \right)}{\sin \left( {\theta + \theta_{1}} \right)}}$ and $r_{s} = \frac{\tan \left( {\theta - \theta_{1}} \right)}{\tan \left( {\theta + \theta_{1}} \right)}$

where q₁ is related to the angle of incidence with respect to the surface normal q by $\frac{\sin (\theta)}{\sin \left( \theta_{1} \right)} = \frac{1}{n_{s}}$

where ns is the index of refraction of the silicon and the incident medium is assumed to be air, with an index of refraction of one.

The carrier concentration dependence of the polarization rotation comes in through the amplitude reflection coefficients r_(s) and r_(p), which are both functions of the complex index of refraction,

 {overscore (n)}=n _(s) +ik  (36)

In semiconductors, the real part is given by $\begin{matrix} {n = {{n_{so} + {\Delta \quad n}} = {{n_{so} - \frac{q^{2}N}{2\quad \varepsilon_{o}n_{so}m^{*}\omega^{2}}} = {n_{so} - \frac{2\quad \pi^{2}q^{2}N\quad \lambda^{2}}{\varepsilon_{o}n_{so}m^{*}c^{2}}}}}} & (37) \end{matrix}$

where n_(s0) is the index of refraction in the absence of carrier concentration N, q is the electron charge, e₀ is the dielectric constant of free space, m* is the effective mass of the carriers, c is the speed of light, l the wavelength, and w is the frequency of the probe light. Equation (37) is found using the Drude theory, described in Jackson.

The imaginary part k relates to the absorption coefficient a and the wavelength λ as $\begin{matrix} {k = \frac{\alpha \quad (\lambda)\lambda}{4\pi}} & (38) \end{matrix}$

In silicon, a has two main components, one due to band-to-band absorption and a second due to free carriers,

α(λ)=α_(bb)(λ)+α_(b)(λ)  (39)

α_(bb) may be looked up in common references. A fit, valid over the wavelength range of 0.4 to 1.5 μm, is

 log₁₀(α(λ))=9.519−19.826λ+23.26λ²−10.857λ³  (40)

An approximate form of the free carrier absorption term in silicon is $\begin{matrix} {\alpha_{f} = {\frac{4N}{10^{17}}\left( \frac{\lambda}{9} \right)^{2}}} & (41) \end{matrix}$

where the wavelength λ is in units of microns and the free carrier concentration N is in units of 1/cm³.

From equations (37) and (41), it is seen that both the real and imaginary parts of the index of refraction are functions of the carrier concentration. Note that the dependence becomes stronger at longer wavelengths, and therefore use of a longer wavelength probe beam is preferred.

The size of the probe beam spot cannot be made arbitrarily large, however, since too large a spot may not fit into patterns in integrated circuits. The diameter of the spot for a gaussian beam is $\begin{matrix} {{2w_{0}} = \frac{1.22\quad \lambda}{NA}} & (42) \end{matrix}$

where the wavelength l is in units of microns and NA is the numerical aperture of the lens. For a wavelength of 0.8 μm and NA of 0.9, the spot size is about 1 μm.

The polarization rotation is measured by interfering the reflected beam with the reference beam. The reference and reflected beams propagate along the same axis to the polarizing beam splitter 1918, which sends sum and difference components to the two detectors 1932 a and 1932 b. The field for the sum component is $\begin{matrix} {E_{+} = \left( {E_{rx} + \frac{E_{ref}}{\sqrt{2}}} \right)} & (43) \end{matrix}$

and for the difference component is $\begin{matrix} {E_{-} = \left( {E_{ry} - \frac{E_{ref}}{\sqrt{2}}} \right)} & (44) \end{matrix}$

The current in each detector is proportional to the incident power, which is the squared magnitude of the electric field. At each illuminated point on the surface of the photocell receiving the sum component there is a power density $\begin{matrix} {P_{+} = {\frac{{E_{ref}}^{2}}{2} + {\frac{E_{ref}}{\sqrt{2}}\left( {E_{rx} + E_{rx}^{*}} \right)} + {E_{rx}}^{2}}} & (45) \end{matrix}$

and on the photocell receiving the difference component there is a power density $\begin{matrix} {P_{-} = {\frac{{E_{ref}}^{2}}{2} - {\frac{E_{ref}}{\sqrt{2}}\left( {E_{ry} + E_{ry}^{*}} \right)} + {{E_{ry}}^{2}.}}} & (46) \end{matrix}$

The net signal current is found by integrating these power densities over each photocell, multiplying by the conversion efficiency A (usually in amps/watt), and subtracting from one another. The result is $\begin{matrix} {I_{netsig} = {A\frac{{\overset{\circ}{E}}_{{ref}\quad}}{\sqrt{2}}{\int_{0}^{2\quad \pi}{\int_{0}^{w}{\left( {E_{rx} + E_{rx}^{*} + E_{ry} + E_{ry}^{*}}\quad \right)r{r}\quad {\varphi}}}}}} & (47) \end{matrix}$

where the terms in E_(rx) ² and E_(ry) ² are neglected as small. The signal current is the difference between the net signal current and the signal current when the generation beam power is zero, given by $\begin{matrix} {I_{sig} = {A{\frac{E_{ref}}{\sqrt{2}}\left\lbrack {{\int_{0}^{2\quad \pi}{\int_{0}^{w}{\left\lbrack \left( {E_{rx} + E_{rx}^{*} + E_{ry} + E_{ry}^{*}}\quad \right) \right\rbrack r{r}\quad {\varphi}}}} - {\int_{0}^{2\quad \pi}{\int_{0}^{w}{\left\lbrack \left( {E_{rx0} + E_{rx0}^{*} + E_{ry0} + E_{ry0}^{*}}\quad \right) \right\rbrack r{r}\quad {\varphi}}}}} \right\rbrack}}} & (48) \end{matrix}$

Shot noise is usually the largest contributor to noise, given by $\begin{matrix} {I_{shot} = {{A\sqrt{\frac{2{qBW}}{A}\left( \frac{P_{1}}{2} \right)}} = \sqrt{{qAP}_{1}{BW}}}} & (49) \end{matrix}$

The factor of two arises because the reference beam is split between the two photocells. The signal-to-noise ratio (SNR) is the ratio I_(sig)/I_(shot).

FIG. 13 illustrates the SNR in dB (10 dB per decade) as a function of the log₁₀ of the doping concentration. The NA is 0.9 and the probe laser power at the silicon and the reference beam powers are both 1 mW. The beam radius is 0.35 cm and the photodetector conversion efficiency is 0.4 A/W, for simplicity assumed independent of wavelength. The noise bandwidth is 0.3 Hz. The background doping concentration is 10¹⁵ for the 10¹⁶ doping point, and 10¹⁶ for the other points.

Graphs of SNR as a function of the log of dosage are shown in FIG. 13 for four wavelengths (0.53 μm for line 2004, 0.67 μm for line 2003 0.83 μm for line 2002, and 1.48 μm for line 2001). The response to doping is linear, and the effect of wavelength is small. Note that the SNR is in the range of 10-20 dB for even the lowest doping, and is greater than 20 dB for doping concentration in excess of 10¹⁷/cm³. The linear nature of line 2001 indicates that the polarized beam measurement can be used in each of the methods discussed above, e.g. in reference to FIGS. 5A-5H.

Numerous modifications and adaptations of the above-described embodiments will become apparent to a person skilled in the art of semiconductor physics. For example, although computer 103C is described as being programmed with one or more specific equations, computer 103C can be programmed with other equations described herein, or with one or more equations that approximate any of the relations between material properties as described herein, for use with measurements performed by profiler 103 while creating a diffusive modulation of charge carriers in a wafer under measurement. For example, an approximate equation used by profiler 103 to measure a material property can be obtained by curve-fitting to measurement data from reference wafers, or by curve-fitting to data obtained from a numerical model, or both depending on the specific implementation.

Therefore, numerous such modifications and adaptations of the above-described embodiments are encompassed by the attached claims. 

What is claimed is:
 1. An apparatus for evaluating a semiconductor wafer comprising: a source of a first beam having a first intensity adequate to excite said semiconductor wafer; an oscillator that modulates said first beam at a frequency in the range of 1 Hz to 20,000 Hz; a source of a second beam having a second intensity; a support for said semiconductor wafer onto which said first and second beams are incident; and a detector onto which a portion of said second beam is incident after interaction of said first and said second beams with said semiconductor wafer.
 2. The apparatus of claim 1 wherein said first beam is selected from the group consisting of photons, ions, and electrons.
 3. The apparatus of claim 1 wherein said semiconductor wafer is of a material having a bandgap energy and wherein said first beam has an energy greater than said bandgap energy and said second beam has an energy less than said bandgap energy.
 4. The apparatus of claim 1 wherein a generation rate is defined by flux per unit area divided by absorption length of a beam incident on said semiconductor wafer, and a generation rate of said first beam is at least an order of magnitude larger than a generation rate of said second beam.
 5. The apparatus of claim 1 wherein said first intensity is substantially equal to said second intensity, and an absorption length of said first beam is less than an absorption length of said second beam.
 6. The apparatus of claim 1 wherein said first intensity is greater than said second intensity.
 7. The apparatus of claim 1 wherein said semiconductor wafer has a doped region.
 8. The apparatus of claim 1 wherein said semiconductor wafer comprises substantially pure silicon.
 9. The apparatus of claim 1 wherein said first beam has a power less than 200 milliwatts and said second beam has a power less than 70 milliwatts.
 10. The apparatus of claim 1 further comprising a computer coupled to said detector, wherein said computer receives a signal from said detector proportional to the intensity of said portion of said second beam incident on said detector.
 11. The apparatus of claim 10 further comprising a processor for forming doped regions in said semiconductor wafer, wherein said processor is coupled to said computer and said computer outputs a signal to said processor to control said processor.
 12. The apparatus of claim 10 further comprising an annealer for annealing said semiconductor wafer, wherein said annealer is coupled to said computer and said computer outputs a signal to said annealer to control said annealer.
 13. The apparatus of claim 1 wherein said source of a second beam comprises a laser.
 14. The apparatus of claim 13 wherein said second beam has a wavelength greater than about 870 nm.
 15. The apparatus of claim 13 wherein said second beam has a wavelength of about 1480 nm.
 16. The apparatus of claim 13 wherein said detector comprises: a photosensitive element; and an amplifier coupled to said photosensitive element and to said oscillator, wherein said amplifier outputs a signal proportional to a measured intensity of said portion of said second beam incident on said photosensitive element.
 17. The apparatus of claim 16 wherein said interaction of said second beam with said semiconductor wafer is reflection and said measured intensity is related to a reflectance of said second beam by said semiconductor wafer.
 18. The apparatus of claim 16 wherein said second beam is polarized and said interaction of said second beam with said semiconductor wafer comprises polarization rotation upon reflection and said measured intensity is related to said polarization rotation.
 19. The apparatus of claim 16 wherein said second beam is incident on said semiconductor wafer at a non-normal angle to said semiconductor wafer and said interaction of said second beam with said semiconductor wafer comprises polarization rotation upon reflection and said measured intensity is related to said polarization rotation.
 20. The apparatus of claim 16 wherein said support is a stage which moves in three dimensions and said semiconductor wafer is thereby moved to a plurality of positions relative to said first and second beams and said signal is determined at each of said positions, whereby a defect level of said semiconductor wafer is determined.
 21. The apparatus of claim 20 further comprising the act of comparing said defect level to a predetermined range.
 22. The apparatus of claim 20 wherein said defect level is the difference between a maximum signal and a minimum signal of said signals determined at each position.
 23. The apparatus of claim 16 wherein a plurality of signals is determined for a plurality of different values of an operation parameter of said apparatus, whereby a value of a property of said semiconductor wafer is determined.
 24. The apparatus of claim 23 wherein said operation parameter is a power of said first beam.
 25. The apparatus of claim 23 wherein said operation parameter is a diameter of said first beam relative to a diameter of said second beam at said semiconductor wafer.
 26. The apparatus of claim 23 wherein said operation parameter is an offset distance between said first beam and said second beam at said semiconductor wafer.
 27. The apparatus of claim 23 wherein said property is selected from a group consisting of mobility, junction depth, surface carrier concentration, doping concentration, lifetime, sheet resistance, and active dopant concentration as a function of depth of said semiconductor wafer.
 28. The apparatus of claim 16 wherein a plurality of signals is determined for a plurality of different values of an operation parameter of said apparatus, whereby a value of a process condition of said semiconductor wafer is determined.
 29. The apparatus of claim 28 wherein said process condition is anneal temperature.
 30. The apparatus of claim 23 wherein said value of said property of said semiconductor wafer is determined by comparing said plurality of signals measured to reference signals.
 31. The apparatus of claim 1 wherein said source of said first beam comprises a laser.
 32. The apparatus of claim 31 wherein a wavelength of said first beam is about 830 nm.
 33. The apparatus of claim 1 further comprising an anamorphic prism located in a path of said first beam between said source of said first beam and said support.
 34. The apparatus of claim 1 further comprising: a combiner located to combine said first beam and said second beam thereby to form a combined beam incident on said semiconductor wafer; a first splitter located to divert a portion of said combined beam reflected by said semiconductor wafer to said detector; and a filter in the path of said portion of said combined beam between said first splitter and said detector, wherein said filter filters said first beam from said portion of said combined beam whereby a filtered portion of said second beam is incident on said detector.
 35. A method for evaluating a semiconductor wafer comprising the acts of: providing a first beam having a first intensity adequate to excite said semiconductor wafer; modulating said first beam at a frequency in the range of 1 Hz to 20,000 Hz; providing a second beam having a second intensity; directing said first and said second beams at said semiconductor wafer; and detecting a portion of said second beam reflected by said semiconductor wafer.
 36. The method of claim 35 wherein said semiconductor wafer has a bandgap energy and wherein said first beam has an energy greater than said bandgap energy and said second beam has an energy less than said bandgap energy.
 37. The method of claim 35 wherein a generation rate is defined by flux per unit area divided by absorption length of a beam incident on said semiconductor wafer, and a generation rate of said first beam is at least an order of magnitude larger than a generation rate of said second beam.
 38. The method of claim 35 wherein said first intensity is substantially equal to said second intensity, and an absorption length of said first beam is less than an absorption length of said second beam.
 39. The method of claim 35 wherein said first intensity is greater than said second intensity.
 40. The method of claim 35 further comprising the acts of: altering a value of an operation parameter of said first or second beam and generating new signal at said altered operation parameter; and repeating said altering of said value of said operation parameter and generating a new signal at said altered value of said operation parameter to generate a plurality of signals.
 41. The method of claim 39 further comprising the act of analyzing said plurality of signals to determine a value of a property of said semiconductor wafer.
 42. The method of claim 40 wherein said property is selected from a group consisting of mobility, junction depth, surface carrier concentration, doping concentration, lifetime, sheet resistance, and active dopant concentration.
 43. The method of claim 40 further comprising the act of analyzing said plurality of signals to determine a value of a process parameter used to process said semiconductor wafer.
 44. The method of claim 43 wherein said process parameter is annealing temperature.
 45. The method of claim 40 wherein said operation parameter is a power of said first beam.
 46. The method of claim 40 wherein said operation parameter is a diameter of said first beam relative to a diameter of said second beam at said semiconductor wafer.
 47. The method of claim 40 wherein said operation parameter is a distance between said first and said second beams at said semiconductor wafer.
 48. The method of claim 40 further comprising the acts of: comparing said value of said property of said semiconductor wafer to a predetermined range; and discarding said semiconductor wafer if said value of said property is outside of said range.
 49. The method of claim 48 further comprising the acts of: sending a control signal to a processing unit that processed said semiconductor wafer; and altering a process condition in said processing unit if said value of said property is outside said predetermined range.
 50. The method of claim 48 further comprising the acts of: sending a control signal in response to a value of said value of said property and altering an annealing of said semiconductor wafer in response to said control signal.
 51. The method of claim 35 further comprising the acts of: detecting a plurality of signals at a plurality of positions of said semiconductor wafer relative to said first and said second beam; and calculating a defect level of said semiconductor wafer from said plurality of signals.
 52. The method of claim 51 further comprising the acts of: comparing said defect level of said semiconductor wafer to a predetermined range; and discarding said semiconductor wafer if said defect level is outside of said predetermined range.
 53. The method of claim 35 wherein said first beam comprises light.
 54. The method of claim 35 wherein saidsecond beamcomprises light.
 55. The method of claim 35 wherein said first source comprises a laser outputting said first beam having a first wavelength and said second source comprises a laser outputting said second beam having a second differing wavelength and wherein said second differing wavelength is greater than about 810 nm.
 56. The apparatus of claim 1, wherein said portion of said second beam is modulated at about said frequency after interaction of said first and second beams with said semiconductor wafer.
 57. The method of claim 35, whereby said second portion of said second beam is modulated at about said frequency after interaction of said first and second beams with said semiconductor wafer. 